文章基本信息

标题：Weak weak quenched limits for the path-valued processes of hitting times and positions of a transient, one-dimensional random walk in a random environment
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作者：Jonathon Peterson ; Gennady Samorodnitsky
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2012
卷号：IX
期号：2
页码：531-569
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In this article we continue the study of the quenched distributions oftransient, one-dimensional random walks in a random environment. In a previousarticle we showed that while the quenched distributions of the hitting times do notconverge to any deterministic distribution, they do have a weak weak limit in thesense that - viewed as random elements of the space of probability measures - theyconverge in distribution to a certain random probability measure (we refer to thisas a weak weak limit because it is a weak limit in the weak topology). Here, weimprove this result to the path-valued process of hitting times. As a consequence,we are able to also prove a weak weak quenched limit theorem for the path of therandom walk itself.
关键词：Weak quenched limits; point process; heavy tails; random probability;measure; probability-valued c`adl`ag functions.