Stochastic variational inequalities with oblique subgradients

Details Stochastic variational inequalities with oblique subgradients Stochastic variational inequalities with oblique subgradients

2011-02-17

arxiv.org/abs/1102.3634v4

Mathematics

Probability

34 pages

Scientific paper

In this paper we will study the existence and uniqueness of the solution for the stochastic variational inequality with oblique subgradients of the following form:{l} dX_{t}+H(X_{t}) \partial \phi (X_{t}) (dt) \ni f(t,X_{t}) dt+g(t,X_{t}) dB_{t},\quad t>0,\smallskip \ X_{0}=x\in \bar{\emph{Dom}(\phi)}.% This problem is the generalization of the stochastic differential equation with oblique reflection considered by Lions and Sznitman in `84. The existence result is based on a deterministic approach; first, we prove the existence and uniqueness of the solution of a differential system with singular input.

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