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Tail probabilities of a random walk on an interval

Author

Listed:
  • Ewa M. Kubicka
  • Grzegorz Kubicki
  • Małgorzata Kuchta
  • Michał Morayne

Abstract

If a random walk starts at the center of a symmetric discrete interval I={−r,…,−1,0,1,…,r} and we condition on being in I until a given time t, then for any fixed s,0≤s≤r, the probability that at time t the random walk is in the tail {−r,…,−s}∪{s,…,r} is non decreasing in t if we assume that either t is always even or t is always odd.

Suggested Citation

  • Ewa M. Kubicka & Grzegorz Kubicki & Małgorzata Kuchta & Michał Morayne, 2021. "Tail probabilities of a random walk on an interval," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(9), pages 2161-2169, May.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:9:p:2161-2169
    DOI: 10.1080/03610926.2019.1662044
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