**CRM Monograph Series**

Volume: 6;
1994;
134 pp;
Hardcover

MSC: Primary 60;
**Print ISBN: 978-0-8218-0269-4
Product Code: CRMM/6**

List Price: $62.00

Individual Member Price: $49.60

# An Introduction to Branching Measure-Valued Processes

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*Eugene B. Dynkin*

A co-publication of the AMS and Centre de Recherches Mathématiques

For about half a century, two classes of stochastic processes—Gaussian processes and processes with independent increments—have played an important role in the development of stochastic analysis and its applications. During the last decade, a third class—branching measure-valued (BMV) processes—has also been the subject of much research. A common feature of all three classes is that their finite-dimensional distributions are infinitely divisible, allowing the use of the powerful analytic tool of Laplace (or Fourier) transforms. All three classes, in an infinite-dimensional setting, provide means for study of physical systems with infinitely many degrees of freedom. This is the first monograph devoted to the theory of BMV processes. Dynkin first constructs a large class of BMV processes, called superprocesses, by passing to the limit from branching particle systems. Then he proves that, under certain restrictions, a general BMV process is a superprocess. A special chapter is devoted to the connections between superprocesses and a class of nonlinear partial differential equations recently discovered by Dynkin.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Table of Contents

# Table of Contents

## An Introduction to Branching Measure-Valued Processes

#### Readership

Research mathematicians and graduate students.

#### Reviews

A reader whose primary interest is in applications to analysis … will find the essentials here in concise form … though perhaps rather daunting at first sight, Dynkin's book becomes more and more user-friendly with acquaintance.

-- Bulletin of the London Mathematical Society

BMV processes are now providing an approach to a delicate analysis of certain nonlinear partial differential equations. This book provides the background needed for the understanding of these new developments.

-- Mathematical Reviews