Bilateral multivalued stochastic integral equations with weakening of the Lipschitz assumption

Abstract

We present a study on multivalued stochastic integral equations whose form contains stochastic Lebesgue integrals and integrals driven by the Wiener processes on both sides of equation. We prove existence and uniqueness of local solution to such equations with drift and diffusion coefficients satisfying a condition which is weaker than the Lipschitz condition. The method of proof is based on a sequence of approximations. Then, continuous dependence of solution on equation's data is shown.