Open Access
Translator Disclaimer
March 2012 Stochastic equations, flows and measure-valued processes
Donald A. Dawson, Zenghu Li
Ann. Probab. 40(2): 813-857 (March 2012). DOI: 10.1214/10-AOP629


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. Poincaré Probab. Statist. 41 (2005) 307–333]. Two scaling limit theorems for the generalized Fleming–Viot 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].


Download Citation

Donald A. Dawson. Zenghu Li. "Stochastic equations, flows and measure-valued processes." Ann. Probab. 40 (2) 813 - 857, March 2012.


Published: March 2012
First available in Project Euclid: 26 March 2012

zbMATH: 1254.60088
MathSciNet: MR2952093
Digital Object Identifier: 10.1214/10-AOP629

Primary: 60G09 , 60J68
Secondary: 60J25 , 92D25

Keywords: Coalescent , Continuous-state branching process , generalized Fleming–Viot process , immigration , Stochastic equation , stochastic flow , Strong solution , Superprocess

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.40 • No. 2 • March 2012
Back to Top