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

2017/12/01 by Jian Song, Song, Jian, Xiaoming Song +3
Economics, Econometrics and Finance · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1712.00475

openalex publication_date 2017/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Anticipating Random Periodic Solutions--II. SPDEs with Multiplicative Linear Noise

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