The Hurst index of long-range dependent renewal processes
成果类型：
Article
署名作者：
Daley, DJ
署名单位：
Australian National University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1022677560
发表日期：
1999
页码：
2035-2041
关键词：
摘要：
A stationary renewal process N(.) for which the lifetime distribution has its hth moment finite or infinite according as k is less than or greater than kappa for some 1 < K < 2, is long-range dependent and has Hurst index alpha = (1/2)(3-kappa) (this is the critical index alpha for which lim sup(t-->infinity) t(-2a) var N(0, t] is finite or infinite according as a is greater than or less than alpha). This identification is accomplished by delineating the growth rate properties of the difference between the renewal function and its linear asymptote, thereby extending work of Tacklind.