THE EXISTENCE AND UNIQUENESS THEOREMS FOR STOCHASTIC DIFFERENTIAL-DIFFERENCE HYBRID SYSTEMS

Abstract

A stochastic differential-difference hybrid system is a system of interacting variables whose dynamics are described by stochastic differential equations for some of them and difference equations for others. Systems with two types of difference equations are examined: first, a difference equation in the form of a process involving the multiplicative Wiener process, and second, a difference equation with delay. The existence and uniqueness theorems for both systems have been proven. The basic conditions on the system’s parameters are local Lipschitz conditions and linear growth order.