On The Martingale Problem For Interactive Measure Valued Branching Diffusions
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On the Martingale Problem for Interactive Measure-Valued Branching Diffusions
Author: Edwin Arend Perkins
language: en
Publisher: American Mathematical Soc.
Release Date: 1995
This book develops stochastic integration with respect to ``Brownian trees'' and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well-posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.
On the Martingale Problem for Interactive Measure-valued Branching Diffusions
Author: Perkins, E. A. (Edwin A.)
language: en
Publisher: Laboratory for Research in Statistics and Probability, Carleton University = Laboratoire de recherche en statistique et probabilités, Carleton University
Release Date: 1993