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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     author = {Glinyanaya E. V.},
     title = {Discrete analogue of the {Krylov--Veretennikov} expansion},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {39--49},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a4/}
}
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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/