An Introduction to Branching Measure-Valued Processes (Crm Monograph Series) by E. B. Dynkin

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Название:An Introduction to Branching Measure-Valued Processes (Crm Monograph Series, Vol 6)

Автор: E. B. Dynkin

Издательство: American Mathematical Society

ISBN: 0821802690

Год:June 22, 1994

Страниц: Pages: 134

Язык:Английский

Формат: DJVU

Размер: 1.16 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.