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July 2004 A stochastic log-Laplace equation
Jie Xiong
Ann. Probab. 32(3B): 2362-2388 (July 2004). DOI: 10.1214/009117904000000540

Abstract

We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term and making use of the particle system representation developed by Kurtz and Xiong [Stochastic Process. Appl. 83 (1999) 103–126]. We also derive the Wong–Zakai type approximation for this equation. As an application, we give a direct proof of the moment formulas of Skoulakis and Adler [Ann. Appl. Probab. 11 (2001) 488–543].

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Jie Xiong. "A stochastic log-Laplace equation." Ann. Probab. 32 (3B) 2362 - 2388, July 2004. https://doi.org/10.1214/009117904000000540

Information

Published: July 2004
First available in Project Euclid: 6 August 2004

zbMATH: 1055.60042
MathSciNet: MR2078543
Digital Object Identifier: 10.1214/009117904000000540

Subjects:
Primary: 60G57 , 60H15
Secondary: 60J80

Keywords: particle system representation , random environment , Stochastic partial differential equation , Superprocess , Wong–Zakai approximation

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 3B • July 2004
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