### STOCHASTIC INCLUSIONS WITH CURRENT VELOCITIES HAVING DECOMPOSABLE RIGHT-HAND SIDES

#### Abstract

An existence of solution theorem is 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, lower semi-continuous but not necessarily have convex images. Instead we suppose that they are decomposable.

#### Keywords

mean derivatives; current velocities; decomposable set-valued mappings; differential inclusions.

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