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Local Properties of Distributions of Stochastic Functionals
Yu. A. Davydov, University of Lille I, Villeneuve d'Ascq, France, M. A. Lifshits, MANCOMTECH Training Center, St. Petersburg, Russia, and N. V. Smorodina, Radiation Hygiene Institute, St. Petersburg, Russia
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Translations of Mathematical Monographs
1998; 184 pp; hardcover
Volume: 173
ISBN-10: 0-8218-0584-3
ISBN-13: 978-0-8218-0584-8
List Price: US$98 Member Price: US$78.40
Order Code: MMONO/173

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.

(i) 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.

(ii) 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.

(iii) 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.

Graduate students and research mathematicians working in the theory of stochastic processes.

Reviews

"A very interesting book."

-- Mathematical Reviews

"[T]his book will be of interest both for specialists working in the area and for students who want to enter this interesting field of research."

-- Zentralblatt MATH

• Preliminaries
• Methods for studying distributions of functionals
• Gaussian functionals
• Poisson functionals
• Local limit theorems
• Bibliographical notes
• Bibliography
• Index