On generalized random differential equations

Abstract

The study of random equations was initiated by the Prague school of probabilists in the Fifties. An account of results on this topic can be found in the books by Bharucha-Reid [lj, Soong [15J, Tsokos and Padgett 06J. In this paper we investigate the generalized differential equation x € <p(to,t,x), where w is a random parameter and </> is a given set-valued mapping. Deterministic equations of this type were studied e.g. by Filippov [a] and Hermes £9]. First results on random differential equations with the multivalued right-hand side were obtained by Castaing DJ, [4] (see also [5]). Phan Van Chuong studied generalized random integral equations (Fragment tekstu).