Spectral analysis of fractional kinetic equations with random data. (English) Zbl 1034.82044

Anh, V. V.; Leonenko, N. N.

J. Stat. Phys. 104, No. 5-6, 1349-1387 (2001).

Summary: We present a spectral representation of the mean-square solution of the fractional kinetic equation (also known as fractional diffusion equation) with random initial condition. Gaussian and non-Gaussian limiting distributions of the renormalized solution of the fractional-in-time and in-space kinetic equation are described in terms of multiple stochastic integral representations.

MSC:

82C40	Kinetic theory of gases in time-dependent statistical mechanics
60G60	Random fields
60H30	Applications of stochastic analysis (to PDEs, etc.)

Keywords:

Mittag-Leffler function; Bessel potential; Riesz potential; spectral representation; mean-square solution; limiting distributions; renormalized solution