Discrete analogue of the Krylov-Veretennikov expansion

Glinyanaya E.V.
Theory of Stochastic Processes
Vol.17 (33), no.1, 2011, pp.39-49
We consider a difference analogue of the stochastic flow with interaction in ${\mathbb R}.$ The discrete-time flow is given by a difference equation with random perturbation which is defined by a sequence of stationary Gaussian processes. We obtain the Ito-Wiener expansion for a solution to the stochastic difference equation which can be regarded as a discrete analogue of the Krylov-Veretennikov representation for a solution to the stochastic differential equation.