Abstract
In the paper we study the existence of solutions of the random differential inclusion
x˙t∈G(t,xt) P.1,t∈[0,T]-a.e.x0=dμ,
where G is a given set-valued mapping value in the space Kn of all nonempty,
compact and convex subsets of the space ℝn, and μ is some probability measure
on the Borel σ-algebra in ℝn. Under certain restrictions imposed on F and μ, 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.