Limit Theorems for Random Walks with Absorption
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).
KeywordsAbsorption time Boundary crossing Conditional limit theorem First passage time Killed random walk Limit theorem Persistence probability Random walk
Mathematics Subject Classification (2010)60G50 60F17
I am very grateful to V. Vysotsky for drawing my attention to the work  and to F. Aurzada for the valuable comments which helped improve the presentation and the clarity of the paper.
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