Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips
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Publication:456207
DOI10.1214/EJP.V17-2216zbMATH Open1261.60070arXiv1109.6453OpenAlexW2156100736MaRDI QIDQ456207
Author name not available (Why is that?)
Publication date: 23 October 2012
Published in: (Search for Journal in Brave)
Abstract: We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non-existence of moments for first-passage and last-exit times. In our proofs we also make use of estimates for hitting probabilities and large deviations bounds. Our results are more general than existing results in the literature, which consider only the case of sums of independent (typically, identically distributed) random variables. We do not assume the Markov property. Existing results that we generalize include a circle of ideas related to the Marcinkiewicz-Zygmund strong law of large numbers, as well as more recent work of Kesten and Maller. Our proofs are robust and use martingale methods. We demonstrate the benefit of the generality of our results by applications to some non-classical models, including random walks with heavy-tailed increments on two-dimensional strips, which include, for instance, certain generalized risk processes.
Full work available at URL: https://arxiv.org/abs/1109.6453
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