Geodesic
The~moment functions for the~solution of the~heat equation with stochastic coefficients
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 2, pp. 351-371

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The formulae of the mean value and the second moment function are obtained for the heat differential equation with stochastic coefficient at the higher derivative, stochastic initial condition and stochastic exterior perturbation. The formulae do not contain the continual integral and hold even for dependent stochastic processes. The expression for the mean value of the solution generalizes the well-known Poisson formula for the solution of the heat differential equation. 
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     author = {V. G. Zadorozhniy},
     title = {The~moment functions for the~solution of the~heat equation with stochastic coefficients},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {351--371},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_2_a3/}
}
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V. G. Zadorozhniy. The~moment functions for the~solution of the~heat equation with stochastic coefficients. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 2, pp. 351-371. http://geodesic.mathdoc.fr/item/FPM_2001_7_2_a3/