Geodesic
On finding moment functions for the solution of the Cauchy problem for the diffusion equation with random coefficients
Izvestiya. Mathematics , Tome 66 (2002) no. 4, pp. 771-788

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We consider the Cauchy problem for the diffusion equation with one spatial variable. The coefficients and the initial data are random processes. Formulae for the first and second moment functions are derived for the solution of the problem. 
@article{IM2_2002_66_4_a3,
     author = {V. G. Zadorozhniy},
     title = {On finding moment functions for the solution of the {Cauchy} problem for the diffusion equation with random coefficients},
     journal = {Izvestiya. Mathematics },
     pages = {771--788},
     publisher = {mathdoc},
     volume = {66},
     number = {4},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_4_a3/}
}
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V. G. Zadorozhniy. On finding moment functions for the solution of the Cauchy problem for the diffusion equation with random coefficients. Izvestiya. Mathematics , Tome 66 (2002) no. 4, pp. 771-788. http://geodesic.mathdoc.fr/item/IM2_2002_66_4_a3/