CRM Monograph Series 1994; 134 pp; hardcover Volume: 6 ISBN10: 0821802690 ISBN13: 9780821802694 List Price: US$62 Member Price: US$49.60 Order Code: CRMM/6
 For about half a century, two classes of stochastic processesGaussian processes and processes with independent incrementshave played an important role in the development of stochastic analysis and its applications. During the last decade, a third classbranching measurevalued (BMV) processeshas also been the subject of much research. A common feature of all three classes is that their finitedimensional distributions are infinitely divisible, allowing the use of the powerful analytic tool of Laplace (or Fourier) transforms. All three classes, in an infinitedimensional 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 copublished with the Centre de Recherches Mathématiques. 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 userfriendly 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  SuperBrownian motion and partial differential equations
 Introduction
 Markov processes
 Construction of superprocesses
 General FeynmanKac formula
 Change of parameters in superprocesses
 Structure of branching measurevalued processes
 Historical notes and comments
 Elements of stochastic calculus
 References
 Index
 Index of notation
