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2020 Stochastic partial integral-differential equations with divergence terms
Chi Hong Wong, Xue Yang, Jing Zhang
Electron. J. Probab. 25: 1-22 (2020). DOI: 10.1214/20-EJP448

Abstract

We study a class of stochastic partial integral-differential equations with an asymmetrical non-local operator $\frac{1} {2}\Delta +a^{\alpha }\Delta ^{\frac{\alpha } {2}}+b\cdot \nabla $ and a distribution expressed as divergence of a measurable field. For $0<\alpha <2$, the existence and uniqueness of solution is proved by analytical method, and a probabilistic interpretation, similar to the Feynman-Kac formula, is presented for $ 0<\alpha <1$. The method of backward doubly stochastic differential equations is also extended in this work.

Citation

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Chi Hong Wong. Xue Yang. Jing Zhang. "Stochastic partial integral-differential equations with divergence terms." Electron. J. Probab. 25 1 - 22, 2020. https://doi.org/10.1214/20-EJP448

Information

Received: 4 October 2018; Accepted: 6 April 2020; Published: 2020
First available in Project Euclid: 28 April 2020

zbMATH: 1445.60049
MathSciNet: MR4092769
Digital Object Identifier: 10.1214/20-EJP448

Subjects:
Primary: 35R60, 60G46, 60H15

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