Spectral analysis of fractional kinetic equations with random data

被引：128

作者：

Anh, VV

Leonenko, NN

机构：

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[2] Cardiff Univ, Sch Math, Cardiff CF2 4YH, S Glam, Wales

[3] Kyiv Univ Natl, Dept Math, UA-252601 Kiev, Ukraine

来源：

JOURNAL OF STATISTICAL PHYSICS | 2001年 / 104卷 / 5-6期

基金：

澳大利亚研究理事会;

关键词：

fractional kinetic equation; fractional diffusion equation; scaling laws; renormalised solution; long-range dependence; non-Gaussian scenario; Mittag-Leffler function; Bessel potential; Riesz potential; stable distributions;

D O I：

10.1023/A:1010474332598

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：1349 / 1387

页数：39

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[1] STRATIFIED STRUCTURE OF THE UNIVERSE AND BURGERS-EQUATION - A PROBABILISTIC APPROACH [J].