Abstract:

The purpose of this report is to present a survey of the theory of Random Equations. It is somewhat a revised version of the paper entitled "On the theory of Random equations" by the author, in the American Mathematical Society Proceedings of symposia in Applied Mathematics: Stochastic processes in mathematical physics and engineering. The study of semigroups of Random operators is initiated and formulated a stochastic analogue of the abstract Cauchy problem  in order to study random solutions of partial differential equations using semigroup theory. This theory when developed should enable us to solve partial differential equations when the differential operator (infinitesimal generator of the semigroup) is a random operator. A detailed discussion of Ito Equation is given in the chapter, 'Random Integral Equations'. 