Probabilistic representation of parabolic stochastic variational inequality with Dirichlet-Neumann boundary and variational generalized backward doubly stochastic differential equations
Probability
2025-01-06 v2
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.
Keywords
Cite
@article{arxiv.2110.00750,
title = {Probabilistic representation of parabolic stochastic variational inequality with Dirichlet-Neumann boundary and variational generalized backward doubly stochastic differential equations},
author = {Yong Ren and Auguste Aman and Qing Zhou},
journal= {arXiv preprint arXiv:2110.00750},
year = {2025}
}
Comments
This version is 39 pages long and has been accepted to Stochastics who will publish the final version