Buch, Englisch, 134 Seiten, Format (B × H): 184 mm x 263 mm, Gewicht: 468 g
Reihe: CRM Monograph Series
Buch, Englisch, 134 Seiten, Format (B × H): 184 mm x 263 mm, Gewicht: 468 g
Reihe: CRM Monograph Series
ISBN: 978-0-8218-0269-4
Verlag: American Mathematical Society
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.
This is the first monograph devoted to the theory of BMV processes. A special chapter is devoted to the connections between superprocesses and a class of nonlinear partial differential equations recently discovered by Dynkin.
