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

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.)
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