STRONG LAWS FOR SMALL INCREMENTS OF RENEWAL PROCESSES

• 成果类型: Article
• 署名作者: STEINEBACH, J
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990234
• 发表日期: 1991
• 页码: 1768-1776
• 关键词: erdos-renyi; LIMIT-THEOREMS

摘要

Let {N(t), t greater-than-or-equal-to 0} be the (generalized) renewal process associated with an i.i.d. sequence X1, X2,... of random variables having finite moment generating function on some left-sided neighborhood of the origin. Some strong limiting results are proved for the maximal increments sup0 less-than-or-equal-to t less-than-or-equal-to T - K (N(t + K) - N(t)), where K = K(T) is a function of T such that K(T) up infinity, but K(T)/log T down 0 as T --> infinity. These provide analogs to a recent extension due to Mason (1989) of the Erdos-Renyi strong law of large numbers for partial sums.