On the martingale problem for interactive measure-valued branching diffusions
Author(s)
Bibliographic Information
On the martingale problem for interactive measure-valued branching diffusions
（Memoirs of the American Mathematical Society, no. 549）
American Mathematical Society, 1995
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Note
"May 1995, volume 115, number 549, (first of 5 numbers)."--T.p
Includes bibliographical references (p. 88-89)
Description and Table of Contents
Description
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.
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