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Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips

Hryniv, Ostap and MacPhee, I.M. and Menshikov, Mikhail V. and Wade, Andrew (2012) Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips. Electronic Journal of Probability, 17 (59). pp. 1-28. ISSN 1083-6489

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    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.

    Item type: Article
    ID code: 40693
    Notes: This has been updated
    Keywords: heavy-tailed random walks, non-homogeneous random walks, transience, rate of escape, passage times, last exit times, semimartingales, random walks on strips, random walks with internal degrees of freedom, risk process, Probabilities. Mathematical statistics, Statistics and Probability, Statistics, Probability and Uncertainty
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 02 Aug 2012 14:52
    Last modified: 27 Mar 2014 22:00
    URI: http://strathprints.strath.ac.uk/id/eprint/40693

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