Limit Theorems for Random Walks with Absorption

Micha Buck ()
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Micha Buck: Technische Universitat Darmstadt

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 241-263

Abstract: 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; 60G50; 60F17 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00970-5

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