Serge Guillas - Academia.edu (original) (raw)

Papers by Serge Guillas

Frontiers in Earth Science

Tsunamis are unpredictable and infrequent but potentially large impact natural disasters. To prep... more Tsunamis are unpredictable and infrequent but potentially large impact natural disasters. To prepare, mitigate and prevent losses from tsunamis, probabilistic hazard and risk analysis methods have been developed and have proved useful. However, large gaps and uncertainties still exist and many steps in the assessment methods lack information, theoretical foundation, or commonly accepted methods. Moreover, applied methods have very different levels of maturity, from already advanced probabilistic tsunami hazard analysis for earthquake sources, to less mature probabilistic risk analysis. In this review we give an overview of the current state of probabilistic tsunami hazard and risk analysis. Identifying research gaps, we offer suggestions for future research directions. An extensive literature list allows for branching into diverse aspects of this scientific approach.

Frontiers in Earth Science

Tsunamis are unpredictable events and catastrophic in their potential for destruction of human li... more Tsunamis are unpredictable events and catastrophic in their potential for destruction of human lives and economy. The unpredictability of their occurrence poses a challenge to the tsunami community, as it is difficult to obtain from the tsunamigenic records estimates of recurrence rates and severity. Accurate and efficient mathematical/computational modeling is thus called upon to provide tsunami forecasts and hazard assessments. Compounding this challenge for warning centres is the physical nature of tsunamis, which can travel at extremely high speeds in the open ocean or be generated close to the shoreline. Thus, tsunami forecasts must be not only accurate but also delivered under severe time constraints. In the immediate aftermath of a tsunamigenic earthquake event, there are uncertainties in the source such as location, rupture geometry, depth, magnitude. Ideally, these uncertainties should be represented in a tsunami warning. However in practice, quantifying the uncertainties i...

. We develop a new method to analyze the total electron content (TEC) depression in the ionospher... more . We develop a new method to analyze the total electron content (TEC) depression in the ionosphere after a tsunami occurrence. We employ Gaussian process regression to accurately estimate the TEC disturbance every 30 s using satellite observations from the GNSS network, even over regions without measurements. We face multiple challenges. First, the impact of the acoustic wave generated by a tsunami onto TEC levels is non-linear and anisotropic. Second, observation points are moving. Third, the measured data is not uniformly distributed in the targeting range. Nevertheless, our method always computes the electron density depression volumes, along with estimated uncertainties, when applied to the 2011 Tohoku-Oki Earthquake, even with random selections of only 5 % of the 1,000 GPS Earth Observation Network System receivers considered here over Japan. Also, the statistically estimated TEC depression area mostly overlaps the range of the initial tsunami, which indicates that our method can potentially be used to estimate the initial tsunami. The method can warn of a tsunami event within 15 minutes of the earthquake, at high levels of confidence, even with a sparse receiver network. Hence, it is potentially applicable worldwide using the existing GNSS network.

<p&amp... more <p>Historical earthquakes in the Java subduction zone have given genesis to tsunami affecting the southwest coasts of the island of Java, in Indonesia. The most recent earthquake on the 17<sup>th</sup> of July 2006, has given rise to a tsunami that killed more than 600 people. The tsunami was difficult to escape due to the small amount of ground shaking, which could have acted as an early warning, and due to the epicentre being very close to the shorelines, giving insufficient time for response. Historical data and scientific studies give little evidence for mega-thrust events in the Java trench, however such possibilities are not excluded and could have a devastating impact in the region. This work aims to assess the tsunami hazard occurring from a range of earthquake scenarios in the subduction zone. Taking as a benchmark the 2006 event, we initially validate our modelling approach against the wave observations recorded at three tide gauges. We then expand our work to account for future earthquake scenarios and their tsunamigenic consequences in the southern coasts of Java island. Bathymetry displacement is computed using the Okada elastic dislocation model. The nonlinear shallow water equation solver JAGURS is employed for the modelling of wave propagation. Our objective is to quantify the uncertainty of such events by using statistical surrogates: fast stochastic approximations of the model that can explore the likelihood of thousands of tsunami scenarios in a few moments of time. Gaussian process emulators are utilised to predict maximum wave amplification occurring from varying parameter distributions such as the moment magnitude of an earthquake. The resulting tsunami hazard footprints can be used in conjunction with existing socio-demographic information to assess tsunami risk in vulnerable areas. The end-data can eventually be used to inform policy making for better disaster mitigation planning.</p>

Journal of the Royal Statistical Society: Series C (Applied Statistics)

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with ... more Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome this challenge, we employ a basis representation of the model outputs and observations: we match these decompositions to carry out the calibration efficiently. In the second step, we incorporate the non-stationary behaviour, in terms of spatial variations of both variance and correlations, in the calibration.We insert two integrated nested Laplace approximation-stochastic partial differential equation parameters into the calibration. A synthetic example and a climate model illustration highlight the benefits of our approach.

Geoscientific Model Development

In this paper, we present the VOLNA-OP2 tsunami model and implementation; a finite-volume nonline... more In this paper, we present the VOLNA-OP2 tsunami model and implementation; a finite-volume nonlinear shallow-water equation (NSWE) solver built on the OP2 domain-specific language (DSL) for unstructured mesh computations. VOLNA-OP2 is unique among tsunami solvers in its support for several high-performance computing platforms: central processing units (CPUs), the Intel Xeon Phi, and graphics processing units (GPUs). This is achieved in a way that the scientific code is kept separate from various parallel implementations, enabling easy maintainability. It has already been used in production for several years; here we discuss how it can be integrated into various workflows, such as a statistical emulator. The scalability of the code is demonstrated on three supercomputers, built with classical Xeon CPUs, the Intel Xeon Phi, and NVIDIA P100 GPUs. VOLNA-OP2 shows an ability to deliver productivity as well as performance and portability to its users across a number of platforms.

The Annals of Applied Statistics

The rarity of tsunamis impels the scientific community to rely on numerical simulation for planni... more The rarity of tsunamis impels the scientific community to rely on numerical simulation for planning and risk assessment purposes because of the low availability of actual data from historic events. Numerical models, also called simulators, typically produce time series of outputs. Due to the large computational cost of such simulators, statistical emulation is required to carry out uncertainty quantification tasks, as emulators efficiently approximate simulators. There is thus a need to create emulators that respect the nature of time series outputs. We introduce here a novel statistical emulation of the inputoutput dependence of these computer models. We employ the Outer Product Emulator with two enhancements. Functional registration and Functional Principal Components techniques improve the predictions of the emulator. Our phase registration method captures fine variations in amplitude. Smoothness in the time series of outputs is modelled, and we are thus able to select more representative, and more parsimonious, regression functions than a fixed basis method such as a Fourier basis. We apply this approach to the high resolution tsunami wave propagation and coastal inundation for the Cascadia region in the Pacific Northwest. The coseismic representation in this analysis is novel, and more realistic than in previous studies. With the help of the emulator, we can carry out sensitivity analysis of the maximum wave elevation with respect to the source characteristics, and we are able to propagate uncertainties from the source characteristics to wave heights in order to issue probabilistic statements about tsunami hazard for Cascadia.

SIAM/ASA Journal on Uncertainty Quantification

High accuracy complex computer models, also called simulators, require large resources in time an... more High accuracy complex computer models, also called simulators, require large resources in time and memory to produce realistic results. Statistical emulators are computationally cheap approximations of such simulators. They can be built to replace simulators for various purposes, such as the propagation of uncertainties from inputs to outputs or the calibration of some internal parameters against observations. However, when the input space is of high dimension, the construction of an emulator can become prohibitively expensive. In this paper, we introduce a joint framework merging emulation with dimension reduction in order to overcome this hurdle. The gradient-based kernel dimension reduction technique is chosen due to its ability to drastically decrease dimensionality with little loss in information. The Gaussian process emulation technique is combined with this dimension reduction approach. Theoretical properties of the approximation are explored. Our proposed approach provides an answer to the dimension reduction issue in emulation for a wide range of simulation problems that cannot be tackled using existing methods. The efficiency and accuracy of the proposed framework is demonstrated theoretically and compared with other methods on an elliptic partial differential equation (PDE) problem. We finally present a realistic application to tsunami modeling. The uncertainties in the bathymetry (seafloor elevation) are modeled as high-dimensional realizations of a spatial process using a geostatistical approach. Our dimension-reduced emulation enables us to compute the impact of these uncertainties on resulting possible tsunami wave heights near-shore and onshore. Considering an uncertain earthquake source, we observe a significant increase in the spread of uncertainties in the tsunami heights due to the contribution of the bathymetry uncertainties to the overall uncertainty budget. These results highlight the need to include the effect of uncertainties in the bathymetry in tsunami early warnings and risk assessments.

Statistical Inference For Stochastic Processes 8 185 204, 2005

Abstract We present the autoregressive Hilbertian with exogenous variables model (ARHX) which int... more Abstract We present the autoregressive Hilbertian with exogenous variables model (ARHX) which intends to take into account the dependence structure of random curves viewed as H-valued random variables, where H is a Hilbert space of functions, under the influence of ...

C R Acad Sci Ser I Math, 2000

de Cachan s'est dotée d'un dispositif immersif 3D stéréoscopique nommé SHIVA, acronyme de SHared ... more de Cachan s'est dotée d'un dispositif immersif 3D stéréoscopique nommé SHIVA, acronyme de SHared Interaction & Visualization Area. Il s'agit principalement d'une dalle murale en verre d'une taille de 5,5 m de longueur par 2 m de hauteur. Deux projecteurs Full HD projettent par l'arrière une image 3D de 3335x1200 pixels offrant une vision stéréoscopique de grand confort par l'intermédiaire de lunettes 3D actives. Le dispositif est également équipé d'un système de tracking infra-rouge permettant le plongement immersif et l'interaction au moyen de joysticks ou de capteurs installés sur le corps humain. L'ensemble est complété par un système de son spatialisé 7.1 et un multiplexeur de flux multimédia. Des travaux ont permis l'intégration de SHIVA dans l'une des grandes salles de l'ENS Cachan, servant autant pour les réunions institutionnelles de l'Ecole (Conseil d'Administration, Conseil scientifique) que dispositif expérimental pour la Recherche et l'Enseignement.

Computer Methods in Applied Mechanics and Engineering 279 536 553, Sep 1, 2014

Comptes Rendus De L Academie Des Sciences Serie Ii Mecanique Physique Chimie Sciences De L Univers Sciences De La Terre, Jul 1, 2000

Reçu le 6 mars 2000, accepté après révision le 11 mai 2000) Résumé. Nous généralisons à des proce... more Reçu le 6 mars 2000, accepté après révision le 11 mai 2000) Résumé. Nous généralisons à des processus à valeurs dans un espace de Banach différentes notions de non-causalité en temps discret et en temps continu. Nous nous intéresserons à la préservation de la non-causalité par discrétisation fonctionnelle d'un processus à trajectoires continues. Enfin, nous établirons des théorèmes limites (loi des grands nombres et théorème central limite) pour des processus autorégressifs hilbertiens d'ordre un avec variables exogènes. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Noncausality and functional discretization, limit theorems for an ARHX(1) process

Journal of Applied Probability, 2002

In this paper, we consider a Hilbert-space-valued autoregressive stochastic sequence (Xn) with se... more In this paper, we consider a Hilbert-space-valued autoregressive stochastic sequence (Xn) with several regimes. We suppose that the underlying process (In) which drives the evolution of (Xn) is stationary. Under some dependence assumptions on (In), we prove the existence of a unique stationary solution, and with a symmetric compact autocorrelation operator, we can state a law of large numbers with rates and the consistency of the covariance estimator. An overall hypothesis states that the regimes where the autocorrelation operator's norm is greater than 1 should be rarely visited.

Statistics & Probability Letters, 2001

... eres (c'est `a dire présentant une forte corrélation `a des intervalles régu... more ... eres (c'est `a dire présentant une forte corrélation `a des intervalles réguliers) peuvent être appréhendées par le mod`ele SARIMA (pour Seasonal ... Barrat et al (1990) [1]. Les données utilisées sont celles de la concentration en NO heure par heure au centre ville de Caen durant ...

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000

Reçu le 6 mars 2000, accepté après révision le 11 mai 2000) Résumé. Nous généralisons à des proce... more Reçu le 6 mars 2000, accepté après révision le 11 mai 2000) Résumé. Nous généralisons à des processus à valeurs dans un espace de Banach différentes notions de non-causalité en temps discret et en temps continu. Nous nous intéresserons à la préservation de la non-causalité par discrétisation fonctionnelle d'un processus à trajectoires continues. Enfin, nous établirons des théorèmes limites (loi des grands nombres et théorème central limite) pour des processus autorégressifs hilbertiens d'ordre un avec variables exogènes. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Noncausality and functional discretization, limit theorems for an ARHX(1) process

Frontiers in Earth Science

Tsunamis are unpredictable and infrequent but potentially large impact natural disasters. To prep... more Tsunamis are unpredictable and infrequent but potentially large impact natural disasters. To prepare, mitigate and prevent losses from tsunamis, probabilistic hazard and risk analysis methods have been developed and have proved useful. However, large gaps and uncertainties still exist and many steps in the assessment methods lack information, theoretical foundation, or commonly accepted methods. Moreover, applied methods have very different levels of maturity, from already advanced probabilistic tsunami hazard analysis for earthquake sources, to less mature probabilistic risk analysis. In this review we give an overview of the current state of probabilistic tsunami hazard and risk analysis. Identifying research gaps, we offer suggestions for future research directions. An extensive literature list allows for branching into diverse aspects of this scientific approach.

Frontiers in Earth Science

Tsunamis are unpredictable events and catastrophic in their potential for destruction of human li... more Tsunamis are unpredictable events and catastrophic in their potential for destruction of human lives and economy. The unpredictability of their occurrence poses a challenge to the tsunami community, as it is difficult to obtain from the tsunamigenic records estimates of recurrence rates and severity. Accurate and efficient mathematical/computational modeling is thus called upon to provide tsunami forecasts and hazard assessments. Compounding this challenge for warning centres is the physical nature of tsunamis, which can travel at extremely high speeds in the open ocean or be generated close to the shoreline. Thus, tsunami forecasts must be not only accurate but also delivered under severe time constraints. In the immediate aftermath of a tsunamigenic earthquake event, there are uncertainties in the source such as location, rupture geometry, depth, magnitude. Ideally, these uncertainties should be represented in a tsunami warning. However in practice, quantifying the uncertainties i...

. We develop a new method to analyze the total electron content (TEC) depression in the ionospher... more . We develop a new method to analyze the total electron content (TEC) depression in the ionosphere after a tsunami occurrence. We employ Gaussian process regression to accurately estimate the TEC disturbance every 30 s using satellite observations from the GNSS network, even over regions without measurements. We face multiple challenges. First, the impact of the acoustic wave generated by a tsunami onto TEC levels is non-linear and anisotropic. Second, observation points are moving. Third, the measured data is not uniformly distributed in the targeting range. Nevertheless, our method always computes the electron density depression volumes, along with estimated uncertainties, when applied to the 2011 Tohoku-Oki Earthquake, even with random selections of only 5 % of the 1,000 GPS Earth Observation Network System receivers considered here over Japan. Also, the statistically estimated TEC depression area mostly overlaps the range of the initial tsunami, which indicates that our method can potentially be used to estimate the initial tsunami. The method can warn of a tsunami event within 15 minutes of the earthquake, at high levels of confidence, even with a sparse receiver network. Hence, it is potentially applicable worldwide using the existing GNSS network.

<p&amp... more <p>Historical earthquakes in the Java subduction zone have given genesis to tsunami affecting the southwest coasts of the island of Java, in Indonesia. The most recent earthquake on the 17<sup>th</sup> of July 2006, has given rise to a tsunami that killed more than 600 people. The tsunami was difficult to escape due to the small amount of ground shaking, which could have acted as an early warning, and due to the epicentre being very close to the shorelines, giving insufficient time for response. Historical data and scientific studies give little evidence for mega-thrust events in the Java trench, however such possibilities are not excluded and could have a devastating impact in the region. This work aims to assess the tsunami hazard occurring from a range of earthquake scenarios in the subduction zone. Taking as a benchmark the 2006 event, we initially validate our modelling approach against the wave observations recorded at three tide gauges. We then expand our work to account for future earthquake scenarios and their tsunamigenic consequences in the southern coasts of Java island. Bathymetry displacement is computed using the Okada elastic dislocation model. The nonlinear shallow water equation solver JAGURS is employed for the modelling of wave propagation. Our objective is to quantify the uncertainty of such events by using statistical surrogates: fast stochastic approximations of the model that can explore the likelihood of thousands of tsunami scenarios in a few moments of time. Gaussian process emulators are utilised to predict maximum wave amplification occurring from varying parameter distributions such as the moment magnitude of an earthquake. The resulting tsunami hazard footprints can be used in conjunction with existing socio-demographic information to assess tsunami risk in vulnerable areas. The end-data can eventually be used to inform policy making for better disaster mitigation planning.</p>

Journal of the Royal Statistical Society: Series C (Applied Statistics)

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with ... more Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome this challenge, we employ a basis representation of the model outputs and observations: we match these decompositions to carry out the calibration efficiently. In the second step, we incorporate the non-stationary behaviour, in terms of spatial variations of both variance and correlations, in the calibration.We insert two integrated nested Laplace approximation-stochastic partial differential equation parameters into the calibration. A synthetic example and a climate model illustration highlight the benefits of our approach.

Geoscientific Model Development

In this paper, we present the VOLNA-OP2 tsunami model and implementation; a finite-volume nonline... more In this paper, we present the VOLNA-OP2 tsunami model and implementation; a finite-volume nonlinear shallow-water equation (NSWE) solver built on the OP2 domain-specific language (DSL) for unstructured mesh computations. VOLNA-OP2 is unique among tsunami solvers in its support for several high-performance computing platforms: central processing units (CPUs), the Intel Xeon Phi, and graphics processing units (GPUs). This is achieved in a way that the scientific code is kept separate from various parallel implementations, enabling easy maintainability. It has already been used in production for several years; here we discuss how it can be integrated into various workflows, such as a statistical emulator. The scalability of the code is demonstrated on three supercomputers, built with classical Xeon CPUs, the Intel Xeon Phi, and NVIDIA P100 GPUs. VOLNA-OP2 shows an ability to deliver productivity as well as performance and portability to its users across a number of platforms.

The Annals of Applied Statistics

The rarity of tsunamis impels the scientific community to rely on numerical simulation for planni... more The rarity of tsunamis impels the scientific community to rely on numerical simulation for planning and risk assessment purposes because of the low availability of actual data from historic events. Numerical models, also called simulators, typically produce time series of outputs. Due to the large computational cost of such simulators, statistical emulation is required to carry out uncertainty quantification tasks, as emulators efficiently approximate simulators. There is thus a need to create emulators that respect the nature of time series outputs. We introduce here a novel statistical emulation of the inputoutput dependence of these computer models. We employ the Outer Product Emulator with two enhancements. Functional registration and Functional Principal Components techniques improve the predictions of the emulator. Our phase registration method captures fine variations in amplitude. Smoothness in the time series of outputs is modelled, and we are thus able to select more representative, and more parsimonious, regression functions than a fixed basis method such as a Fourier basis. We apply this approach to the high resolution tsunami wave propagation and coastal inundation for the Cascadia region in the Pacific Northwest. The coseismic representation in this analysis is novel, and more realistic than in previous studies. With the help of the emulator, we can carry out sensitivity analysis of the maximum wave elevation with respect to the source characteristics, and we are able to propagate uncertainties from the source characteristics to wave heights in order to issue probabilistic statements about tsunami hazard for Cascadia.

SIAM/ASA Journal on Uncertainty Quantification

High accuracy complex computer models, also called simulators, require large resources in time an... more High accuracy complex computer models, also called simulators, require large resources in time and memory to produce realistic results. Statistical emulators are computationally cheap approximations of such simulators. They can be built to replace simulators for various purposes, such as the propagation of uncertainties from inputs to outputs or the calibration of some internal parameters against observations. However, when the input space is of high dimension, the construction of an emulator can become prohibitively expensive. In this paper, we introduce a joint framework merging emulation with dimension reduction in order to overcome this hurdle. The gradient-based kernel dimension reduction technique is chosen due to its ability to drastically decrease dimensionality with little loss in information. The Gaussian process emulation technique is combined with this dimension reduction approach. Theoretical properties of the approximation are explored. Our proposed approach provides an answer to the dimension reduction issue in emulation for a wide range of simulation problems that cannot be tackled using existing methods. The efficiency and accuracy of the proposed framework is demonstrated theoretically and compared with other methods on an elliptic partial differential equation (PDE) problem. We finally present a realistic application to tsunami modeling. The uncertainties in the bathymetry (seafloor elevation) are modeled as high-dimensional realizations of a spatial process using a geostatistical approach. Our dimension-reduced emulation enables us to compute the impact of these uncertainties on resulting possible tsunami wave heights near-shore and onshore. Considering an uncertain earthquake source, we observe a significant increase in the spread of uncertainties in the tsunami heights due to the contribution of the bathymetry uncertainties to the overall uncertainty budget. These results highlight the need to include the effect of uncertainties in the bathymetry in tsunami early warnings and risk assessments.

Statistical Inference For Stochastic Processes 8 185 204, 2005

Abstract We present the autoregressive Hilbertian with exogenous variables model (ARHX) which int... more Abstract We present the autoregressive Hilbertian with exogenous variables model (ARHX) which intends to take into account the dependence structure of random curves viewed as H-valued random variables, where H is a Hilbert space of functions, under the influence of ...

C R Acad Sci Ser I Math, 2000

de Cachan s'est dotée d'un dispositif immersif 3D stéréoscopique nommé SHIVA, acronyme de SHared ... more de Cachan s'est dotée d'un dispositif immersif 3D stéréoscopique nommé SHIVA, acronyme de SHared Interaction & Visualization Area. Il s'agit principalement d'une dalle murale en verre d'une taille de 5,5 m de longueur par 2 m de hauteur. Deux projecteurs Full HD projettent par l'arrière une image 3D de 3335x1200 pixels offrant une vision stéréoscopique de grand confort par l'intermédiaire de lunettes 3D actives. Le dispositif est également équipé d'un système de tracking infra-rouge permettant le plongement immersif et l'interaction au moyen de joysticks ou de capteurs installés sur le corps humain. L'ensemble est complété par un système de son spatialisé 7.1 et un multiplexeur de flux multimédia. Des travaux ont permis l'intégration de SHIVA dans l'une des grandes salles de l'ENS Cachan, servant autant pour les réunions institutionnelles de l'Ecole (Conseil d'Administration, Conseil scientifique) que dispositif expérimental pour la Recherche et l'Enseignement.

Computer Methods in Applied Mechanics and Engineering 279 536 553, Sep 1, 2014

Comptes Rendus De L Academie Des Sciences Serie Ii Mecanique Physique Chimie Sciences De L Univers Sciences De La Terre, Jul 1, 2000

Reçu le 6 mars 2000, accepté après révision le 11 mai 2000) Résumé. Nous généralisons à des proce... more Reçu le 6 mars 2000, accepté après révision le 11 mai 2000) Résumé. Nous généralisons à des processus à valeurs dans un espace de Banach différentes notions de non-causalité en temps discret et en temps continu. Nous nous intéresserons à la préservation de la non-causalité par discrétisation fonctionnelle d'un processus à trajectoires continues. Enfin, nous établirons des théorèmes limites (loi des grands nombres et théorème central limite) pour des processus autorégressifs hilbertiens d'ordre un avec variables exogènes. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Noncausality and functional discretization, limit theorems for an ARHX(1) process

Journal of Applied Probability, 2002

In this paper, we consider a Hilbert-space-valued autoregressive stochastic sequence (Xn) with se... more In this paper, we consider a Hilbert-space-valued autoregressive stochastic sequence (Xn) with several regimes. We suppose that the underlying process (In) which drives the evolution of (Xn) is stationary. Under some dependence assumptions on (In), we prove the existence of a unique stationary solution, and with a symmetric compact autocorrelation operator, we can state a law of large numbers with rates and the consistency of the covariance estimator. An overall hypothesis states that the regimes where the autocorrelation operator's norm is greater than 1 should be rarely visited.

Statistics & Probability Letters, 2001

... eres (c'est `a dire présentant une forte corrélation `a des intervalles régu... more ... eres (c'est `a dire présentant une forte corrélation `a des intervalles réguliers) peuvent être appréhendées par le mod`ele SARIMA (pour Seasonal ... Barrat et al (1990) [1]. Les données utilisées sont celles de la concentration en NO heure par heure au centre ville de Caen durant ...

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000

Reçu le 6 mars 2000, accepté après révision le 11 mai 2000) Résumé. Nous généralisons à des proce... more Reçu le 6 mars 2000, accepté après révision le 11 mai 2000) Résumé. Nous généralisons à des processus à valeurs dans un espace de Banach différentes notions de non-causalité en temps discret et en temps continu. Nous nous intéresserons à la préservation de la non-causalité par discrétisation fonctionnelle d'un processus à trajectoires continues. Enfin, nous établirons des théorèmes limites (loi des grands nombres et théorème central limite) pour des processus autorégressifs hilbertiens d'ordre un avec variables exogènes. © 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Noncausality and functional discretization, limit theorems for an ARHX(1) process