Superprocesses with spatial interactions in a random medium

Hardeep S. Gill

Stochastic Processes and their Applications, 2009, vol. 119, issue 12, 3981-4003

Abstract: We construct a class of interactive measure-valued diffusions driven by a historical super-Brownian motion and an independent white noise by solving a certain stochastic equation. In doing so, we show that the approach of Perkins (2002) [3] can be used to study the problem examined by Dawson et al. (2001) [1]. This unifies and extends both Dawson et al. (2001) [1] and Perkins (2002) [3] and establishes a new class of measure-valued diffusions. The existence and pathwise uniqueness of the solutions are proved, and the solutions are shown to satisfy the natural martingale problem.

Keywords: Dawson-Watanabe; superprocesses; Interactive; measure-valued; diffusions; Historical; super-Brownian; motion; Stochastic; processes; Martingale; problem (search for similar items in EconPapers)
Date: 2009
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