Yury A. Kutoyants's Books

Introduction to the Statistics of Poisson Processes and Applications

By: Yury A. Kutoyants

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Introduction to the Statistics of Poisson Processes and Applications

By: Yury A. Kutoyants

This book covers an extensive class of models involving inhomogeneous Poisson processes and deals with their identification, i.e. the solution of certain estimation or hypothesis testing problems based on the given dataset. These processes are mathematically easy-to-handle and appear in numerous disciplines, including astronomy, biology, ecology, geology, seismology, medicine, physics, statistical mechanics, economics, image processing, forestry, telecommunications, insurance and finance, reliability, queuing theory, wireless networks, and localisation of sources. Beginning with the definitions and properties of some fundamental notions (stochastic integral, likelihood ratio, limit theorems, etc.), the book goes on to analyse a wide class of estimators for regular and singular statistical models. Special attention is paid to problems of change-point type, and in particular cusp-type change-point models, then the focus turns to the asymptotically efficient nonparametric estimation of the mean function, the intensity function, and of some functionals. Traditional hypothesis testing, including some goodness-of-fit tests, is also discussed. The theory is then applied to three classes of problems: misspecification in regularity (MiR),corresponding to situations where the chosen change-point model and that of the real data have different regularity; optical communication with phase and frequency modulation of periodic intensity functions; and localization of a radioactive (Poisson) source on the plane using K detectors. Each chapter concludes with a series of problems, and state-of-the-art references are provided, making the book invaluable to researchers and students working in areas which actively use inhomogeneous Poisson processes.

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Page Count

683

Publisher

Springer Nature

Published Date

ISBN 10

3031370546

ISBN 13

9783031370540

Statistical Inference for Ergodic Diffusion Processes

By: Yury A. Kutoyants

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Statistical Inference for Ergodic Diffusion Processes

By: Yury A. Kutoyants

The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.

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Page Count

493

Publisher

Springer Science & Business Media

Published Date

ISBN 10

144713866X

ISBN 13

9781447138662

Identification of Dynamical Systems with Small Noise

By: Yury A. Kutoyants

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Identification of Dynamical Systems with Small Noise

By: Yury A. Kutoyants

Small noise is a good noise. In this work, we are interested in the problems of estimation theory concerned with observations of the diffusion-type process Xo = Xo, 0 ~ t ~ T, (0. 1) where W is a standard Wiener process and St(') is some nonanticipative smooth t function. By the observations X = {X , 0 ~ t ~ T} of this process, we will solve some t of the problems of identification, both parametric and nonparametric. If the trend S(-) is known up to the value of some finite-dimensional parameter St(X) = St((}, X), where (} E e c Rd , then we have a parametric case. The nonparametric problems arise if we know only the degree of smoothness of the function St(X), 0 ~ t ~ T with respect to time t. It is supposed that the diffusion coefficient c is always known. In the parametric case, we describe the asymptotical properties of maximum likelihood (MLE), Bayes (BE) and minimum distance (MDE) estimators as c --+ 0 and in the nonparametric situation, we investigate some kernel-type estimators of unknown functions (say, StO,O ~ t ~ T). The asymptotic in such problems of estimation for this scheme of observations was usually considered as T --+ 00 , because this limit is a direct analog to the traditional limit (n --+ 00) in the classical mathematical statistics of i. i. d. observations. The limit c --+ 0 in (0. 1) is interesting for the following reasons.

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Page Count

308

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401110204

ISBN 13

9789401110204

Book's by Yury A. Kutoyants

Introduction to the Statistics of Poisson Processes and Applications

Introduction to the Statistics of Poisson Processes and Applications

Statistical Inference for Ergodic Diffusion Processes

Statistical Inference for Ergodic Diffusion Processes

Identification of Dynamical Systems with Small Noise

Identification of Dynamical Systems with Small Noise

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