GIBBS-COX RANDOM FIELDS AND BURGERS TURBULENCE

被引：27

作者：

Funaki, T. ^{[1
]}

Surgailis, D. ^{[2
]}

Woyczynski, W. A. ^{[3
,4
]}

机构：

[1] Nagoya Univ, Dept Math, Nagoya, Aichi 46401, Japan

[2] Lithuania Acad Sci, Inst Math & Informat, LT-2600 Vilnius, Lithuania

[3] Case Western Reserve Univ, Dept Stat, Cleveland, OH 44106 USA

[4] Case Western Reserve Univ, Ctr Stochast & Chaot Proc Sci & Technol, Cleveland, OH 44106 USA

来源：

ANNALS OF APPLIED PROBABILITY | 1995年 / 5卷 / 02期

基金：

美国国家科学基金会;

关键词：

Burgers turbulence; scaling limits; Gibbs-Cox random field; multiple Wiener-Ito integral;

D O I：

10.1214/aoap/1177004774

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：

We study the large time behavior of random fields which are solutions of a nonlinear partial differential equation, called Burgers' equation, under stochastic initial conditions. These are assumed to be of the shot noise type with the Gibbs-Cox process driving the spatial distribution of the "bumps." In certain cases, this work extends an earlier effort by Surgailis and Woyczynski, where only noninteracting "bumps" driven by the traditional doubly stochastic Poisson process were considered. In contrast to the previous work by Bulinski and Molchanov, a non-Gaussian scaling limit of the statistical solutions is discovered. Burgers' equation is known to describe various physical phenomena such as nonlinear and shock waves, distribution of self-gravitating matter in the universe and so forth.

引用

页码：461 / 492

页数：32

共 59 条

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