Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 4, Pages 393-396
doi:10.1155/S1048953395000359
On weak solutions of random differential inclusions
Technical University, Institute of Mathematics, Podgorna 50, Zielona Gora 65-246, Poland
Received 1 January 1995; Revised 1 April 1995
Copyright © 1995 Mariusz Michta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.