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arXiv · 2110.00750

Probabilistic representation of parabolic stochastic variational inequality with Dirichlet-Neumann boundary and variational generalized backward doubly stochastic differential equations

Yong Ren·Auguste Aman·Qing Zhou
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Abstract

We derive the existence and uniqueness of the generalized backward doubly stochastic differential equation with sub-differential of a lower semi-continuous convex function under a non Lipschitz condition. This study allows us give a probabilistic representation (in stochastic viscosity sense) to the parabolic variational stochastic partial differential equations with Dirichlet-Neumann conditions.

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Yong Ren, Auguste Aman, Qing Zhou. 2021-10-02. Probabilistic representation of parabolic stochastic variational inequality with Dirichlet-Neumann boundary and variational generalized backward doubly stochastic differential equations. https://doi.org/10.1080/17442508.2025.2449646

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