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

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en Carte Paperback – 15 Jun 1994
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 thepowerful 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 largeclass 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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ISBN-13: 9780821802694
ISBN-10: 0821802690
Pagini: 134
Ilustrații: references, indexes
Dimensiuni: 184 x 263 x 13 mm
Greutate: 0.47 kg
Ediția: UK ed
Editura: American Mathematical Society
Colecția CRM Monograph Series
Seria CRM Monograph Series

Locul publicării: Oxford, United States