An Introduction to Branching Measure-Valued Processes

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An Introduction to Branching Measure-Valued Processes (Crm Monograph Series) by Eugene B. Dynkin
English | June 22, 1994 | ISBN: 0821802690 | Pages: 134 | DJVU | 1,2 MB

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.

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