A stochastic log-Laplace equation
Probability
2016-09-07 v1
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].
Keywords
Cite
@article{arxiv.math/0410164,
title = {A stochastic log-Laplace equation},
author = {Jie Xiong},
journal= {arXiv preprint arXiv:math/0410164},
year = {2016}
}
Comments
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000540