A stochastic log-Laplace equation
- Xiong, Jie
2010 Mathematics Subject Classification
- 60G57 60H15 60J80
- Superprocess, random environment, Wong-Zakai approximation, particle system representation, stochastic partial differential equation.
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 (1999). 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 (2001).