ON EXISTENCE OF SOLUTIONS TO STOCHASTIC DIFFERENTIAL INCLUSIONS WITH CURRENT VELOCITIES II

Abstract

Existence of solution theorems are obtained for stochastic differential inclusions given in terms of the so-called current velocities (symmetric mean derivatives, a direct analogs of ordinary velocity of deterministic systems) and quadratic mean derivatives (giving information on the diffusion coefficient) on the flat $n$-dimensional torus. Right-hand sides in both the current velocity part and the quadratic part are set-valued but satisfy some natural conditions, under which they have $\varepsilon$-approximations that point-wise converge to Borel measurable selections of the corresponding set-valued mappings.