An introduction to branching measure-valued processes / Eugene B. Dynkin.

Format:

Book

Author/Creator:

Dynkin, E. B. (Evgeniĭ Borisovich), 1924-2014, author.

Series:

CRM monograph series ; Volume 6.

CRM Monograph Series ; Volume 6

Language:

English

Subjects (All):

Branching processes.

Markov processes.

Physical Description:

1 online resource (135 pages) : illustrations.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1994.

Summary:

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.

Notes:

Includes bibliographical references and indexes.

Description based on print version record.

ISBN:

1-4704-3852-6