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On weak solutions of random differential inclusions

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  • Mariusz Michta

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 .

Suggested Citation

  • Mariusz Michta, 1995. "On weak solutions of random differential inclusions," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-4, January.
    • Handle: RePEc:hin:jnijsa:802365
    DOI: 10.1155/S1048953395000359
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