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A note on the simple random walk on : Probability of exiting sequences of sets

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  • Volkov, Stanislav

Abstract

In this note we establish that the probability that the simple random walk on returns to its origin before leaving a strip of width L has asymptotically the same probability as the one for hitting the origin before exiting the centered box of the same size. We also generalize this theorem for fairly arbitrary sequences of increasing sets in .

Suggested Citation

  • Volkov, Stanislav, 2006. "A note on the simple random walk on : Probability of exiting sequences of sets," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 891-897, May.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:9:p:891-897
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