Particle representations of superprocesses with dependent motions
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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.
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
Stochastic Processes and their Applications
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