MEAN-FIELD MODELS IN THE THEORY OF RANDOM-MEDIA .3.

In the mean-field (nonlocal) diffusion approximation, when the Laplacian triangle on the lattice Z(d) is replaced by the corresponding operator triangleBAR V in a volume V subset-of Z(d) (\V\ --> in infinity) [1, 2], a study is made of the t --> infinity asymptotics of the statistical moments (moment functions) m(p) = m(p)(xi,..., x(p), t) = <psi(xi, t, omega) ... psi(x(p), t, omega)>, p = 1, 2,..., for the evolution equation partial derivative psi/partial derivative t = chi-DELTA-V-psi + xi-psi with nonstationary random potential xi = xi(x, t, omega). The case when xi represents Gaussian white noise (with respect to t) is considered in the paper. At the same time, the evolution equation in such a medium is understood in the sense of Ito triple-overdot. In space, the potential-xi is assumed either to be localized, xi(x, t, omega) = delta(x0, x)xi(x0, t, omega), or homogeneous, namely, delta-correlated with respect to x. Under these conditions, the exponent-gamma-p [GRAPHICS] is calculated.