Unusually large values for spectrally positive stable and related processes
成果类型：
Article
署名作者：
O'Brien, GL
署名单位：
York University - Canada
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1022677393
发表日期：
1999
页码：
990-1008
关键词：
摘要：
Two classes of processes are considered. One is a class of spectrally positive infinitely divisible processes which includes all such stable processes. The other is a class of processes constructed from the sequence of partial sums of independent identically distributed positive random variables. A condition analogous to regular variation of the tails is imposed. Then a large deviation principle and a Strassen-type law of the iterated logarithm are presented. These theorems focus on unusually large values of the processes. They are expressed in terms of Skorokhod's M-1 topology.