Nonlinear Feynman-Kac formulae for SPDEs with space-time noise

Jian Song; Xiaoming Song; Qi Zhang

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arXiv · 1712.00475

Nonlinear Feynman-Kac formulae for SPDEs with space-time noise

Jian Song·Xiaoming Song·Qi Zhang

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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.

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Jian Song, Xiaoming Song, Qi Zhang. 2017-12-01. Nonlinear Feynman-Kac formulae for SPDEs with space-time noise. https://arxiv.org/abs/1712.00475

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