Modeste N'zi - Academia.edu (original) (raw)

Papers by Modeste N'zi

Random Operators and Stochastic Equations, 1997

Our aim is to study the following new type of multivalued backward stochastic differential equati... more Our aim is to study the following new type of multivalued backward stochastic differential equation: −dY (t) + ∂ϕ (Y (t)) dt ∋ F (t, Y (t) , Z (t) , Yt, Zt) dt + Z (t) dW (t) , 0 ≤ t ≤ T, Y (T) = ξ , where ∂ϕ is the subdifferential of a convex function and (Yt, Zt) := (Y (t + θ), Z(t + θ)) θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong & Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.

Annales mathématiques Blaise Pascal, 1997

L'accès aux archives de la revue « Annales mathématiques Blaise Pascal » (http:// math.univ-bpcle... more L'accès aux archives de la revue « Annales mathématiques Blaise Pascal » (http:// math.univ-bpclermont.fr/ambp/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ STRASSEN THEOREM IN HOLDER NORM FOR SOME BROWNIAN FUNCTIONALS MODESTE N'ZI

Journal of Mathematics Research, Jun 22, 2021

In this paper, a class of periodic stochastic differential equations driven by general counting p... more In this paper, a class of periodic stochastic differential equations driven by general counting processes (SDEsGp) is studied. First, an existence-uniqueness result for the solution of general SDEsGp based on Poisson processes with τperiodic stochastic intensity of time t has been given, for some τ > 0. Then, using the properties of periodic Markov processes, sufficient conditions for the existence and uniqueness of a periodic solution of the considered equations are obtained. We will then apply the obtained results to the propagation of malaria in a periodic environment.

Journal of advances in mathematics and computer science, Oct 28, 2019

This work was carried out in collaboration between all authors. Author Modeste designed the study... more This work was carried out in collaboration between all authors. Author Modeste designed the study, analyzed the analyses of the study and all the revisions of the manuscript. Author Eric managed the analyses of the study, wrote the draft and final copies of the manuscript and writing numerical simulations. All authors read and approved the final manuscript.

Comptes rendus de l'Académie des sciences, Jun 1, 1997

We prove a Strassen's law of the iterated logarithm at zero for L&y's area process. Contrary to t... more We prove a Strassen's law of the iterated logarithm at zero for L&y's area process. Contrary to the Brownian case, the time inversion argument doesn't seem to work. Here, the main tool in the proof is large deviations estimates for diffusion processes with small diffusion coefficients. Loi locale du logurithme it&G de Strassen pour l'aire de L&y R&sum& Nous montroas une loi de Strussen en zero pour le processus de l'aire de L&y Contrairement au cas brownien, I'argument de l'inversion du temps semble ne pas marcher. Ici. la dtfmmonstrution utilisr les ~grundes de'viations pour les processus de d$fusion i2 co@icienrs de d$fusion petits.

Stochastic Processes and their Applications, Feb 1, 1993

For n 2 2 an (n-I)-parameter real process V,,, called stochastic volume, is defined. This process... more For n 2 2 an (n-I)-parameter real process V,,, called stochastic volume, is defined. This process is an extension to higher dimensions of L&y's stochastic area which is obtained from V,, by setting n = 2. For V,, a Strassen-type functional law of the iterated logarithm is proved by making use of large deviations techniques.

Journal of Applied Mathematics and Stochastic Analysis, 2004

We prove an existence and uniqueness result for backward stochastic differential equations whose ... more We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in a Markovian framework, that is coupled with a forward SDE, our result provides a probabilistic interpretation of solutions to nonlinear PDEs.

arXiv (Cornell University), Apr 3, 2023

This paper studies the distribution function of the time of extinction of a subcritical epidemic,... more This paper studies the distribution function of the time of extinction of a subcritical epidemic, when a large enough proportion of the population has been immunized and/or the infectivity of the infectious individuals has been reduced, so that the effective reproduction number is less than one. We do that for a SIR/SEIR model, where infectious individuals have an infection age dependent infectivity, as in the model introduced in the 1927 seminal paper of Kermack and McKendrick [9]. Our main conclusion is that simplifying the model as an ODE SIR model, as it is largely done in the epidemics literature, introduces a biais toward shorter extinction time.

Stochastics and Stochastics Reports, Aug 1, 2004

We determine the limil under weak convergence of certain normalized partial sums of stationary va... more We determine the limil under weak convergence of certain normalized partial sums of stationary variables with regularly varying covariance. It is shown thai in some Besov spaces the limit process is the fractional Brownian molion.

Random Operators and Stochastic Equations, 2008

Abstract We prove an existence and uniqueness result for backward doubly stochastic differential ... more Abstract We prove an existence and uniqueness result for backward doubly stochastic differential equations whose coefficients satisfy non-Lipschitz assumptions.

HAL (Le Centre pour la Communication Scientifique Directe), Dec 17, 2009

Journal of Applied Mathematics and Stochastic Analysis, 2003

We consider reflected backward stochastic differential equations with time and space dependent co... more We consider reflected backward stochastic differential equations with time and space dependent coefficients in an orthant, and with oblique reflection. Existence and uniqueness of solution are established assuming local Lipschitz continuity of the drift, Lipschitz continuity and uniform spectral radius conditions on the reflection matrix.

Random Operators and Stochastic Equations, 2014

By using large deviation techniques, we prove a Strassen type law of the iterated logarithm for a... more By using large deviation techniques, we prove a Strassen type law of the iterated logarithm for a forward-backward stochastic di erential equation.

$Research paper thumbnail of Approximation of fractional Brownian sheet by a random walk in anisotropic Besov space$

Random Operators and Stochastic Equations, Jan 20, 2007

Under the topology of anisotropic Besov spaces, we prove the convergence in law of a random walk ... more Under the topology of anisotropic Besov spaces, we prove the convergence in law of a random walk defined by the partial sums of a mean zero stationary Gaussian fields to the fractional Brownian sheet.

Random Operators and Stochastic Equations, Mar 1, 2016

In this paper, we present an SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model... more In this paper, we present an SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with a saturated incidence rate and disease causing death in a population of varying size. We define a parameter ℜ * from which a study of stability is made. In the deterministic case, we discuss the existence of an endemic equilibria and prove the global stability of the disease-free equilibrium. By introducing a perturbation in the contact rate through a white noise, we consider a stochastic version. We prove the existence of a global positive solution which lives in a certain domain. Thereafter, we prove the global stability nth moment of the system as soon as the intensity of the white noise is below a certain threshold. Finally, we perform some numerical simulations to compare the dynamic behaviors of the deterministic system and the stochastic system.

Applicationes Mathematicae, 1997

By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in H... more By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.

Stochastics and Stochastics Reports, Apr 1, 1997

We deal with a one dimensional multivalued backward stochastic differential equation associated t... more We deal with a one dimensional multivalued backward stochastic differential equation associated to the subdifferential ∂hof a lower semi-continuous convex function h, with a local lipschitz coefficient (drift). When the terminal value is bounded, we prove the existence of a solution by using a suitable approximation of the drift by a double sequence of lipschitz functions. The uniqueness is obtained

Computational Statistics & Data Analysis, Nov 1, 2006

The combination of road accident frequencies before and after a similar change at a given number ... more The combination of road accident frequencies before and after a similar change at a given number of sites are considered. Each target site includes different accident types and is linked to a specific control area. At any one target site it is assumed that the total number of accidents recorded is multinomially distributed between the before period and the after period and also between several mutually exclusive types. The parameter of the distribution depends on the different accident risks in the control area linked to each site as well as on the average effect of the change. A method of estimating simultaneously the average effect and the accident risks in control areas is suggested. Some simulated accidents data allow us to study the existence and consistence of the linear constrained estimator of the unknown vector parameter.

In this paper, we are interested in solving generalized backward stochastic dierential equation w... more In this paper, we are interested in solving generalized backward stochastic dierential equation with one barrier (RGBSDE for short). We deal with the case of xed terminal and also the random terminal case. The study use some new technical aspects of the stochastic calculus related to the reected Generalized BSDE, (see [5] for the case of BSDE) to derive a priori estimates and prove existence and uniqueness of solution in L p , p > 1. The result extended the one of Aman et al [1]. The need for this type of extension comes from the desire to prove a probabilistic representation of L p − solution of semi-linear partial dierential equation with nonlinear Neumann boundary condition when p ∈ (1, 2).

In this paper, we study backward stochastic nonlinear Volterra integral equations. Under local Li... more In this paper, we study backward stochastic nonlinear Volterra integral equations. Under local Lipschitz continuity condition on the drift, we prove existence and uniqueness result. We also established a stability property for this kind of equations.