LIMIT BEHAVIOR OF QUADRATIC-FORMS OF MOVING AVERAGES AND STATISTICAL SOLUTIONS OF THE BURGERS-EQUATION

JOURNAL OF MULTIVARIATE ANALYSIS

卷:52

Article

关键词: QUADRATIC FORMS;    MOVING AVERAGES;    BURGERS EQUATION;   

DOI  :  10.1006/jmva.1995.1002

来源: Elsevier

【 摘 要 】

Let ..., X(-1), X(0), X(1), ... be symmetric i.i.d. random variables belonging to the domain of normal attraction of an a-stable distribution with 1 < alpha < 2, and let c(j) = j(-beta) Lambda(j) with 1/alpha < beta and a slowly varying Lambda(j). We study the limit behavior of the partial sum processes D-n(t) = Sigma(k=1)([nt]) Q(Sigma(-infinity)(k) c((k-j)) X(j)), where Q(x) is a secondorder polynomial. We also comment on how our result relates to the study of the Burgers' equation with random initial data. (C) 1995 Academic Press, Inc.

【 授权许可】

Free