**Translations of Mathematical Monographs**

1998;
184 pp;
Hardcover

MSC: Primary 60;
**Print ISBN: 978-0-8218-0584-8
Product Code: MMONO/173**

List Price: $103.00

Individual Member Price: $82.40

# Local Properties of Distributions of Stochastic Functionals

Share this page
*Yu. A. Davydov; M. A. Lifshits; N. V. Smorodina*

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.

#### Table of Contents

# Table of Contents

## Local Properties of Distributions of Stochastic Functionals

#### Readership

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