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Limit Theorems for Random Walks with Absorption

  • Micha BuckEmail author
Article

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).

Keywords

Absorption time Boundary crossing Conditional limit theorem First passage time Killed random walk Limit theorem Persistence probability Random walk 

Mathematics Subject Classification (2010)

60G50 60F17 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Technische Universitat DarmstadtDarmstadtGermany

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