Renormalization and homogenization of fractional diffusion equations with random data

被引：33

作者：

Anh, VV

Leonenko, NN

机构：

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

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

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2002年 / 124卷 / 03期

关键词：

fractional diffusion equation; scaling laws; renomialised solution; long-range dependence; non-Gaussian scenario; Mittag-Leffler function; stable distributions; bessel potential; riesz potential;

D O I：

10.1007/s004400200217

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper presents a renormalization and homogenization theory for fractional-in-space or in-time diffusion equations with singular random initial conditions. The spectral representations for the solutions of these equations are provided. Gaussian and non-Gaussian limiting distributions of the renormalized. solutions of these equations are then described in terms of multiple stochastic integral representations.

引用

页码：381 / 408

页数：28