Superprocesses over a stochastic flow

• 成果类型: Article
• 署名作者: Skoulakis, G; Adler, RJ
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2001
• 页码: 488-543
• 关键词: valued branching diffusions; differential-equations

摘要

We study a specific particle system in which particles undergo random branching and spatial motion. Such systems are best described, mathematically, via measure valued stochastic processes. As is now quite standard, we study the so-called superprocess limit of such a system as both the number of particles in the system and the branching rate tend to infinity. What differentiates our system from the classical superprocess case, in which the particles move independently of each other, is that the motions of our particles are affected by the presence of a global stochastic flow. We establish weak convergence to the solution of a well-posed martingale problem. Using the particle picture formulation of the flow superprocess, we study some of its proper-ties. We give formulas for its first two moments and consider two macroscopic quantities describing its average behavior, properties that have been studied in some detail previously in the pure flow situation, where branching was absent. Explicit formulas for these quantities are given and graphs are presented for a specific example of a linear flow of Ornstein-Uhlenbeck type.