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An Introduction to Branching Measure-Valued Processes
Eugene B. Dynkin, Cornell University, Ithaca, NY
A co-publication of the AMS and Centre de Recherches Mathématiques.

CRM Monograph Series
1994; 134 pp; hardcover
Volume: 6
ISBN-10: 0-8218-0269-0
ISBN-13: 978-0-8218-0269-4
List Price: US$59
Member Price: US$47.20
Order Code: CRMM/6
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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.


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

Table of Contents

  • Super-Brownian motion and partial differential equations
  • Introduction
  • Markov processes
  • Construction of superprocesses
  • General Feynman-Kac formula
  • Change of parameters in superprocesses
  • Structure of branching measure-valued processes
  • Historical notes and comments
  • Elements of stochastic calculus
  • References
  • Index
  • Index of notation
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