Geodesic
Mean-field models in~the theory of~random media.~II
Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 1, pp. 143-154

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A study is made of a stationary random medium described by the evolution equation $\partial\psi/\partial t=\varkappa\overline\Delta_V+\xi(\mathbf x)\psi$ where $\overline\Delta_V$ is the operator of mean-field diffusion in the volume $V\subset\mathbf Z^d$, $\xi(\mathbf x),\mathbf x\in V$, are independent random variables with normal distribution $\mathbf N(0,\sigma^2)$. A study is made of the asymptotic behavior of the solution $\psi(\mathbf x,t)$ and its statistical moments $m_p(\mathbf x,t)=\langle\psi^p(\mathbf x,t)\rangle$, $p=1,2,\dots$, as $t\to\infty$, $|V|\to\infty$. The paper continues the earlier [1]. 
@article{TMF_1990_82_1_a14,
     author = {L. V. Bogachev and S. A. Molchanov},
     title = {Mean-field models in~the theory of~random {media.~II}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {143--154},
     publisher = {mathdoc},
     volume = {82},
     number = {1},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_82_1_a14/}
}
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L. V. Bogachev; S. A. Molchanov. Mean-field models in~the theory of~random media.~II. Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 1, pp. 143-154. http://geodesic.mathdoc.fr/item/TMF_1990_82_1_a14/