STOCHASTIC EQUATIONS, FLOWS AND MEASURE-VALUED PROCESSES

• 成果类型: Article
• 署名作者: Dawson, Donald A.; Li, Zenghu
• 署名单位: Carleton University; Beijing Normal University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP629
• 发表日期: 2012
• 页码: 813-857
• 关键词: coalescent

摘要

We first prove some general results on pathwise uniqueness, comparison property and existence of nonnegative strong solutions of stochastic equations driven by white noises and Poisson random measures. The results are then used to prove the strong existence of two classes of stochastic flows associated with coalescents with multiple collisions, that is, generalized Fleming-Viot flows and flows of continuous-state branching processes with immigration. One of them unifies the different treatments of three kinds of flows in Bertoin and Le Gall [Ann. Inst. H. Poincare Probab. Statist. 41 (2005) 307-333]. Two scaling limit theorems for the generalized Fleming-Viol flows are proved, which lead to sub-critical branching immigration superprocesses. From those theorems we derive easily a generalization of the limit theorem for finite point motions of the flows in Bertoin and Le Gall [Illinois J. Math. 50 (2006) 147-181].