An Introduction to Branching Measure-Valued Processes (CRM Monograph Series) - Hardcover

American Mathematical Society

Hardcover

ISBN 10: 0821802690 ISBN 13: 9780821802694

Publisher: American Mathematical Society, 1994

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1994
• Language: English
• ISBN 10: 0821802690
• ISBN 13: 9780821802694
• Binding: Hardcover