On existence of solutions of multivalued stochastic differential equations with discontinuous coefficients

Abstract

The subject of the paper is to find existence conditions of weak solutions to multivalued stochastic differential equations with discontinuous coefficients. First we prove that a non-exploding solution exists when the drift coefficient b satisfies linear growth and the diffusion coefficient σ is uniformly elliptic. On this basis, we continue to obtain a solution (up to the explosion time) in the weak sense under certain local integrability, improving the result of Rozkosz and Słomiński.