Existence and Uniqueness Theorems for Stochastic Differential-Difference Hybrid Systems

A stochastic differential-difference hybrid system is a system of coupled variables whosedynamics is described by stochastic differential equations for some of them and differenceequations for the others. Systems with two types of difference equations are examined: first,a difference equation in the form of a process involving a multiplicative Wiener process, andsecond, a difference equation with delay. The existence and uniqueness theorems for both systemsare proved. The basic conditions on the system’s parameters are local Lipschitz conditions andlinear growth order.