**Translations of Mathematical Monographs**

1990;
180 pp;
Hardcover

MSC: Primary 60;
**Print ISBN: 978-0-8218-4538-7
Product Code: MMONO/83**

List Price: $93.00

Individual Member Price: $74.40

# Generalized Diffusion Processes

Share this page
*Portenko*

Diffusion processes serve as a mathematical model for the physical
phenomenon of diffusion. One of the most important problems in the theory of
diffusion processes is the development of methods for constructing these
processes from a given diffusion matrix and a given drift vector. Focusing on
the investigation of this problem, this book is intended for specialists in
the theory of random processes and its applications.

A generalized diffusion process (that is, a continuous Markov process for
which the Kolmogorov local characteristics exist in the generalized sense)
can serve as a model for diffusion in a medium moving in a nonregular way. The
author constructs generalized diffusion processes under two assumptions:
first, that the diffusion matrix is sufficiently regular; and second, that
the drift vector is a function integrable to some power, or is a generalized
function of the type of the derivative of a measure.