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Limit Theorems for Random Walks with Absorption

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  • Micha Buck

    (Technische Universitat Darmstadt)

Abstract

We introduce a class of absorption mechanisms and study the behavior of real-valued centered random walks with finite variance that do not get absorbed. Our main results serve as a toolkit which allows obtaining persistence and scaling limit results for many different examples in this class. Further, our results reveal new connections between results in Kemperman (The passage problem for a stationary Markov chain. Statistical research monographs, The University of Chicago Press, Chicago, 1961) and Vysotsky (Stoch Processes Appl 125(5):1886–1910, 2015).

Suggested Citation

  • Micha Buck, 2021. "Limit Theorems for Random Walks with Absorption," Journal of Theoretical Probability, Springer, vol. 34(1), pages 241-263, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00970-5
    DOI: 10.1007/s10959-019-00970-5
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    References listed on IDEAS

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    1. Vysotsky, Vladislav, 2015. "Limit theorems for random walks that avoid bounded sets, with applications to the largest gap problem," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1886-1910.
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