Recurrence Properties of a Special Type of Heavy-Tailed Random Walk |
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Authors: | Péter Nándori |
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Institution: | 1.Institute of Mathematics,Budapest University of Technology and Economics,Budapest,Hungary |
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Abstract: | In the proof of the invariance principle for locally perturbed periodic Lorentz process with finite horizon, a lot of delicate
results were needed concerning the recurrence properties of its unperturbed version. These were analogous to the similar properties
of Simple Symmetric Random Walk. However, in the case of Lorentz process with infinite horizon, the analogous results for
the corresponding random walk are not known, either. In this paper, these properties are ascertained for the appropriate random
walk (this happens to be in the non normal domain of attraction of the normal law). As a tool, an estimation of the remainder
term in the local limit theorem for the corresponding random walk is computed. |
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Keywords: | |
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