Particle representations of superprocesses with dependent motions

Kathryn E. Temple

Stochastic Processes and their Applications, 2010, vol. 120, issue 11, 2174-2189

Abstract: We establish Donnelly-Kurtz-type particle representations for a class of superprocesses with dependent spatial motions, and for a sequence of such superprocesses we prove convergence of the finite-dimensional distributions given convergence of the motion processes. As special cases, we construct a superprocess with coalescing spatial motion (SCSM) and a superprocess with dependent spatial motion (SDSM), where the underlying motion processes are one-dimensional coalescing and dependent Brownian motions, respectively. Under suitable conditions on the functions governing the interactions, we show convergence in distribution in of a sequence of SDSMs to an SCSM.

Keywords: Particle; representation; Superprocess; Dependent; motions; Coalescing; Brownian; motion; Interacting; Brownian; flow (search for similar items in EconPapers)
Date: 2010
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