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 ProcessesShare this page
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
Research mathematicians and graduate students.
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