Stochastic partial differential equations associated with Feller processes

2023/10/28 by Jian Song, Meng Wang, Song, Jian +3 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2310.18726

openalex publication_date 2023/10/28 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28

Abstract

For the stochastic partial differential equation (∂ u)/(∂ t)=\mathcal L u +u W where W is Gaussian noise colored in time and \mathcal L is the infinitesimal generator of a Feller process X, we obtain Feynman-Kac type of representations for the Stratonovich and Skorohod solutions as well as for their moments. The regularity of the law and the Hölder continuity of the solutions are also studied.

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• Feynman-Kac formula gor general time dependent stochastic parabolic equation on a bounded domain and applications

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