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Superprocesses with spatial interactions in a random medium

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  • Gill, Hardeep S.

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.

Suggested Citation

  • Gill, Hardeep S., 2009. "Superprocesses with spatial interactions in a random medium," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 3981-4003, December.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:12:p:3981-4003
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    References listed on IDEAS

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    1. Donald A. Dawson & Zenghu Li & Hao Wang, 2001. "Superprocesses with Dependent Spatial Motion and General Branching Densities," RePAd Working Paper Series lrsp-TRS346, Département des sciences administratives, UQO.
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