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
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
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