Abstract
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.
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Chen, X. (2000). On the Law of the Iterated Logarithm for Local Times of Recurrent Random Walks. In: Giné, E., Mason, D.M., Wellner, J.A. (eds) High Dimensional Probability II. Progress in Probability, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1358-1_16
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DOI: https://doi.org/10.1007/978-1-4612-1358-1_16
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