Local properties of distributions of stochastic functionals
著者
書誌事項
Local properties of distributions of stochastic functionals
（Translations of mathematical monographs, v. 173）
American Mathematical Society, c1998
- タイトル別名
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Lokalʹnye svoĭstva raspredeleniĭ stokhasticheskikh funkt︠s︡ionalov
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注記
"Translated from the Russian by V.E. Nazaĭkinskiĭ and M.A. Shishkova" -- T.p. verso
Includes bibliographical references (p. 175-181) and index
内容説明・目次
内容説明
This book investigates the distributions of functionals defined on the sample paths of stochastic processes. It contains systematic exposition and applications of three general research methods developed by the authors. The method of stratifications is used to study the problem of absolute continuity of distribution for different classes of functionals under very mild smoothness assumptions. It can be used also for evaluation of the distribution density of the functional. The method of differential operators is based on the abstract formalism of differential calculus and proves to be a powerful tool for the investigation of the smoothness properties of the distributions. The superstructure method, which is a later modification of the method of stratifications, is used to derive strong limit theorems (in the variation metric) for the distributions of stochastic functionals under weak convergence of the processes.Various application examples concern the functionals of Gaussian, Poisson and diffusion processes as well as partial sum processes from the Donsker-Prokhorov scheme. The research methods and basic results in this book are presented here in monograph form for the first time. The text would be suitable for a graduate course in the theory of stochastic processes and related topics.
目次
Preliminaries Methods for studying distributions of functionals Gaussian functionals Poisson functionals Local limit theorems Bibliographical notes Bibliography Index.
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