On weak solutions of random differential inclusions. (1995) - Michta, Mariusz
Abstract : In the paper we study the existence of solutions of the random differential inclusion x ˙ t ∈ G ( t, x t ) P .1, t ∈ [ 0, T ] - a .e . x 0 = d μ, where G is a given set-valued mapping value in the space K n of all nonempty, compact and convex subsets of the space ℝ n, and μ is some probability measure on the Borel σ -algebra in ℝ n . 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 .