On weak solutions of random differential inclusions

[摘要] In the paper we study the existence of solutions of the random differential inclusionx˙t∈G(t,xt)     P.1,t∈[0,T]-a.e.x0=dμ,whereGis a given set-valued mapping value in the spaceKnof all nonempty, compact and convex subsets of the spaceℝn, andμis some probability measure on the Borelσ-algebra inℝn. Under certain restrictions imposed onFandμ, we obtain weak solutions of problem (I), where the initial condition requires that the solution of (I) has a given distribution at timet=0.

[学科分类] 应用数学