Law of the Iterated Logarithm for Random Walks on Nilpotent Groups
نویسندگان
چکیده
منابع مشابه
On the Law of the Iterated Logarithm for Local Times of Recurrent Random Walks
We consider the law of the iterated logarithm (LIL) for the local time of one-dimensional recurrent random walks. First we show that the constants in the LIL for the local time and for its supremum (with respect to the space variable) are equal under a very general condition given in Jain and Pruitt (1984). Second we evaluate the common value of the constants, as the random walk is in the domai...
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Let α([0,1]) denote the intersection local time of p independent d-dimensional Brownian motions running up to the time 1. Under the conditions p(d− 2)< d and d≥ 2, we prove lim t→∞ t −1 logP{α([0,1])≥ t}=−γα(d, p) with the right-hand side being identified in terms of the the best constant of the Gagliardo–Nirenberg inequality. Within the scale of moderate deviations, we also establish the preci...
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متن کاملOn the law of the iterated logarithm.
The law of the iterated logarithm provides a family of bounds all of the same order such that with probability one only finitely many partial sums of a sequence of independent and identically distributed random variables exceed some members of the family, while for others infinitely many do so. In the former case, the total number of such excesses has therefore a proper probability distribution...
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2001
ISSN: 1350-7265
DOI: 10.2307/3318728