Geodesic
On existence of solutions to stochastic differential inclusions with current velocities II
Journal of computational and engineering mathematics, Tome 3 (2016) no. 1, pp. 48-60

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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.
Keywords: mean derivatives, current velocities, differential inclusions. 
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Yu. E. Gliklikh; A. V. Makarova. On existence of solutions to stochastic differential inclusions with current velocities II. Journal of computational and engineering mathematics, Tome 3 (2016) no. 1, pp. 48-60. http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a5/