Elena Shmileva - Academia.edu (original) (raw)

Papers by Elena Shmileva

arXiv (Cornell University), Jun 26, 2013

We introduce basic statistical methods for the extrapolation of stationary random fields. For squ... more We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non-Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging.

ArXiv, 2021

This work is devoted to the clustering of check-in sequences from a geosocial network. We used th... more This work is devoted to the clustering of check-in sequences from a geosocial network. We used the mixture Markov chain process as a mathematical model for time-dependent types of data. For clustering, we adjusted the ExpectationMaximization (EM) algorithm. As a result, we obtained highly detailed communities (clusters) of users of the now defunct geosocial network, Weeplaces.

Теория вероятностей и ее применения, 2001

В данной работе описаны необходимые и достаточные условия квазиинвариантности распределений пуасс... more В данной работе описаны необходимые и достаточные условия квазиинвариантности распределений пуассоновских мер на X х R + (X-произвольное измеримое пространство) относительно широ кой группы растяжений пространства по компоненте R+. Пока зано также, что класс квазиинвариантных мер далеко не исчер пывается мерами, абсолютно непрерывными относительно рассмо тренной в [1] и [2] гамма-меры. Приведен критерий абсолютной непрерывности одной пуассоновской меры на произвольном изме римом пространстве относительно другой. Ключевые слова и фразы: пуассоновская мера, спектральная мера, квазиинвариантность распределения пуассоновской меры, гамма-мера, расстояние Хеллингера-Какутани. * С.-Петербургский государственный университет, механико-математический фа культет, Библиотечная пл.,

Lecture Notes in Mathematics, 2014

We introduce basic statistical methods for the extrapolation of stationary random fields. For squ... more We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non-Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging.

Theory of Probability & Its Applications, 2002

In this work the necessary and sufficient conditions are given for the quasi-invariance of the di... more In this work the necessary and sufficient conditions are given for the quasi-invariance of the distributions of Poisson measures on XtimesmathbfR+X\times\mathbf R^+XtimesmathbfR+ (for arbitrary measurable space~X) with respect to a large group of the scalings of the component~$\mathbf R^+$. It is shown that the class of quasi-invariant measures is far from being exhausted by the measures absolutely continuous with respect to the gamma measure considered in [N. Tsilevich and A. Vershik, C. R. Acad. Sci. Paris Ser. I Math., 329 (1999), pp. 163--168] and [N. Tsilevich, A. Vershik, and M. Yor, Prepublication 575, Universites Paris VI & Paris VII, Paris, 2000]. A criterion is given for the absolute continuity of a Poisson measure with respect to another Poisson measure on an arbitrary measurable space.

Russian Mathematical Surveys, 2001

Journal of Multivariate Analysis, 2013

In this paper, we discuss three extrapolation methods for α-stable random fields with α ∈ (1, 2].... more In this paper, we discuss three extrapolation methods for α-stable random fields with α ∈ (1, 2]. We justify them, giving proofs of the existence and uniqueness of the solutions for each method and providing sufficient conditions for path continuity. Two methods are based on minimizing the variability of the difference between the predictor and the theoretical value, whereas in the third approach we provide a new method that maximizes the covariation between these two quantities.

Успехи математических наук, 2001

Let X α be a symmetric α-stable Lévy process with α ∈ (1, 2). We consider small ball probabilitie... more Let X α be a symmetric α-stable Lévy process with α ∈ (1, 2). We consider small ball probabilities of the following type P { X α − λ f < r} as r → 0 and λr α−1 → 0 or λr α−1 = c, c > 0, where • is the sup-norm and f is any continuous function which starts at 0. We obtain an exact rate of decrease for these probabilities including constants. Using these small ball estimates, we derive a functional LIL for X α with continuous attracting functions. It occurs that the a.s. limit set of the family Xα(T •) T 1/α h(T) T >0 is equal to the set of all continuous functions (which start at 0), under certain choice of scaling function h(T).

arXiv (Cornell University), Jun 26, 2013

We introduce basic statistical methods for the extrapolation of stationary random fields. For squ... more We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non-Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging.

ArXiv, 2021

This work is devoted to the clustering of check-in sequences from a geosocial network. We used th... more This work is devoted to the clustering of check-in sequences from a geosocial network. We used the mixture Markov chain process as a mathematical model for time-dependent types of data. For clustering, we adjusted the ExpectationMaximization (EM) algorithm. As a result, we obtained highly detailed communities (clusters) of users of the now defunct geosocial network, Weeplaces.

Теория вероятностей и ее применения, 2001

В данной работе описаны необходимые и достаточные условия квазиинвариантности распределений пуасс... more В данной работе описаны необходимые и достаточные условия квазиинвариантности распределений пуассоновских мер на X х R + (X-произвольное измеримое пространство) относительно широ кой группы растяжений пространства по компоненте R+. Пока зано также, что класс квазиинвариантных мер далеко не исчер пывается мерами, абсолютно непрерывными относительно рассмо тренной в [1] и [2] гамма-меры. Приведен критерий абсолютной непрерывности одной пуассоновской меры на произвольном изме римом пространстве относительно другой. Ключевые слова и фразы: пуассоновская мера, спектральная мера, квазиинвариантность распределения пуассоновской меры, гамма-мера, расстояние Хеллингера-Какутани. * С.-Петербургский государственный университет, механико-математический фа культет, Библиотечная пл.,

Lecture Notes in Mathematics, 2014

We introduce basic statistical methods for the extrapolation of stationary random fields. For squ... more We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non-Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging.

Theory of Probability & Its Applications, 2002

In this work the necessary and sufficient conditions are given for the quasi-invariance of the di... more In this work the necessary and sufficient conditions are given for the quasi-invariance of the distributions of Poisson measures on XtimesmathbfR+X\times\mathbf R^+XtimesmathbfR+ (for arbitrary measurable space~X) with respect to a large group of the scalings of the component~$\mathbf R^+$. It is shown that the class of quasi-invariant measures is far from being exhausted by the measures absolutely continuous with respect to the gamma measure considered in [N. Tsilevich and A. Vershik, C. R. Acad. Sci. Paris Ser. I Math., 329 (1999), pp. 163--168] and [N. Tsilevich, A. Vershik, and M. Yor, Prepublication 575, Universites Paris VI & Paris VII, Paris, 2000]. A criterion is given for the absolute continuity of a Poisson measure with respect to another Poisson measure on an arbitrary measurable space.

Russian Mathematical Surveys, 2001

Journal of Multivariate Analysis, 2013

In this paper, we discuss three extrapolation methods for α-stable random fields with α ∈ (1, 2].... more In this paper, we discuss three extrapolation methods for α-stable random fields with α ∈ (1, 2]. We justify them, giving proofs of the existence and uniqueness of the solutions for each method and providing sufficient conditions for path continuity. Two methods are based on minimizing the variability of the difference between the predictor and the theoretical value, whereas in the third approach we provide a new method that maximizes the covariation between these two quantities.

Успехи математических наук, 2001

Let X α be a symmetric α-stable Lévy process with α ∈ (1, 2). We consider small ball probabilitie... more Let X α be a symmetric α-stable Lévy process with α ∈ (1, 2). We consider small ball probabilities of the following type P { X α − λ f < r} as r → 0 and λr α−1 → 0 or λr α−1 = c, c > 0, where • is the sup-norm and f is any continuous function which starts at 0. We obtain an exact rate of decrease for these probabilities including constants. Using these small ball estimates, we derive a functional LIL for X α with continuous attracting functions. It occurs that the a.s. limit set of the family Xα(T •) T 1/α h(T) T >0 is equal to the set of all continuous functions (which start at 0), under certain choice of scaling function h(T).