Nonlinear Feynman-Kac formulae for SPDEs with space-time noise
Probability
2017-12-05 v1
Abstract
We study a class of backward doubly stochastic differential equations (BDSDEs) involving martingales with spatial parameters, and show that they provide probabilistic interpretations (Feynman-Kac formulae) for certain semilinear stochastic partial differential equations (SPDEs) with space-time noise. As an application of the Feynman-Kac formulae, random periodic solutions and stationary solutions to certain SPDEs are obtained.
Keywords
Cite
@article{arxiv.1712.00475,
title = {Nonlinear Feynman-Kac formulae for SPDEs with space-time noise},
author = {Jian Song and Xiaoming Song and Qi Zhang},
journal= {arXiv preprint arXiv:1712.00475},
year = {2017}
}