The growth of additive processes
成果类型：
Article
署名作者：
Yang, Ming
署名单位：
Columbia University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117906000000593
发表日期：
2007
页码：
773-805
关键词：
摘要：
Let X-t be any additive process in R-d. There are finite indices delta(i), beta(i), i = 1. 2 and a function u, all of which are defined in terms of the characteristics of X-t, such that lim(t -> 0) inf u(t)X--1/n(t)* = {0, if n > delta(1), {infinity, if n < delta(2), lim(t -> 0) sup u(t)X--1/n(t)* = {0, if n > beta(2), a.s., {infinity, if n < beta(1), where X-t(*) = sup(0 < s < t) |X-s|. When X-t is a Levy process with X-0 = 0, delta 1 = delta 2, beta 1 = beta 2 and u(t) = t. This is a special case obtained by Pruitt. When X-t is not a Levy process, its characteristics are complicated functions of t. However, there are interesting conditions under which u becomes sharp to achieve delta 1 = delta 2, beta 1 = beta 2.