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The oscillating random walk

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  • Kemperman, J. H. B.

Abstract

{Yn;n=0, 1, ...} denotes a stationary Markov chain taking values in Rd. As long as the process stays on the same side of a fixed hyperplane E0, it behaves as an ordinary random walk with jump measure [mu] or [nu], respectively. Thus ordinary random walk would be the special case [mu] = [nu]. Also the process Y'n = Y'n-1-Zn (with the Zn as i.i.d. real random varia bles) may be regarded as a special case. The general process is studied by a Wiener-Hopf type method. Exact formulae are obtained for many quantities of interest. For the special case that the Yn are integral-valued, renewal type conditions are established which are necessary and sufficient for recurrence.

Suggested Citation

  • Kemperman, J. H. B., 1974. "The oscillating random walk," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 1-29, January.
    • Handle: RePEc:eee:spapps:v:2:y:1974:i:1:p:1-29
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    Cited by:

    1. Ben-Ari, Iddo & Merle, Mathieu & Roitershtein, Alexander, 2009. "A random walk on with drift driven by its occupation time at zero," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2682-2710, August.
    2. Kloas, Judith & Woess, Wolfgang, 2019. "Multidimensional random walk with reflections," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 336-354.
    3. Mikhail V. Menshikov & Dimitri Petritis & Andrew R. Wade, 2018. "Heavy-Tailed Random Walks on Complexes of Half-Lines," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1819-1859, September.

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