Geodesic
Discrete analogue of the Krylov--Veretennikov expansion
Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 39-49.

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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 Itô–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.
Keywords: Random interaction systems, discrete-time flow, Itô–Wiener series expansion. 
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Glinyanaya E. V. Discrete analogue of the Krylov--Veretennikov expansion. Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 39-49. http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a4/

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