GIBBS-COX RANDOM FIELDS AND BURGERS TURBULENCE
成果类型：
Article
署名作者：
Funaki, T.; Surgailis, D.; Woyczynski, W. A.
署名单位：
Nagoya University; Vilnius University; University System of Ohio; Case Western Reserve University; University System of Ohio; Case Western Reserve University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004774
发表日期：
1995
页码：
461-492
关键词：
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.