Title
Particle representations of superprocesses with dependent motions
Document Type
Article
Department or Administrative Unit
Mathematics
Publication Date
11-2010
Abstract
We establish Donnelly–Kurtz-type particle representations for a class of superprocesses with dependentspatial motions, and for a sequence of such superprocesses we prove convergence of the finite-dimensionaldistributions given convergence of the motion processes. As special cases, we construct a superprocesswith 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 convergencein distribution inDP(R)[0,∞)of a sequence of SDSMs to an SCSM.
Recommended Citation
Temple, K. E. (2010). Particle representations of superprocesses with dependent motions. Stochastic Processes and Their Applications, 120(11), 2174–2189. https://doi.org/10.1016/j.spa.2010.06.005
Journal
Stochastic Processes and their Applications
Copyright
© 2010 Elsevier B.V. All rights reserved.
Comments
This article was originally published in Stochastic Processes and their Applications. The full-text article from the publisher can be found here.
Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.