Anh, V. V.; Leonenko, N. N. Spectral analysis of fractional kinetic equations with random data. (English) Zbl 1034.82044 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. Cited in 96 Documents 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 PDF BibTeX XML Cite \textit{V. V. Anh} and \textit{N. N. Leonenko}, J. Stat. Phys. 104, No. 5--6, 1349--1387 (2001; Zbl 1034.82044) Full Text: DOI OpenURL