ON WEAK SOLUTIONS OF RANDOM DIFFERENTIAL INCLUSIONS

In the paper we study the existence of solutions of the random differential in-clusion 2t a(t, xt) P.l,t [0,T]-a.e. (z) x0 #, where G is a given set-valued mapping value in the space Kn of all nonempty, compact and convex subsets of the space n, and # is some probability measure on the Borel a-algebra in Rn. Under certain restrictions imposed on F and #, we obtain weak solutions of problem (I), where the initial condition requires that the solution of (I) has a given distribution at time t 0