On weak solutions of random differential inclusions. (1995)

• Record Type: Journal Article
• Authors: Michta, Mariusz
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 8:Number 4(1995)
• Page Start: 393
• Page End: 396
• Publication Date: 1995
• Subjects: set-valued mappings -- Hukuchara's derivative -- Aumann's integral -- tightness and weak convergence of probability measures; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953395000359
• Languages: English
• ISSNs: 1048-9533

Abstract

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 .