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Limit Theorems for Random Walks with Absorption

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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).

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Acknowledgements

I am very grateful to V. Vysotsky for drawing my attention to the work [9] and to F. Aurzada for the valuable comments which helped improve the presentation and the clarity of the paper.

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  1. Technische Universitat Darmstadt, Darmstadt, Germany

    Micha Buck

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  1. Micha Buck
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Buck, M. Limit Theorems for Random Walks with Absorption. J Theor Probab 34, 241–263 (2021). https://doi.org/10.1007/s10959-019-00970-5

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  • DOI: https://doi.org/10.1007/s10959-019-00970-5

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