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 domain of attraction of a not necessarily symmetric stable law. The first problem relies on a special maximal inequality established in this paper and the second on the LIL for Markovian additive functionals given in the author’s recent work.
KeywordsRandom Walk Local Time Iterate Logarithm Symmetric Stable Process Levy Process
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