The oscillating random walk

J. H. B. Kemperman

Stochastic Processes and their Applications, 1974, vol. 2, issue 1, 1-29

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.

Date: 1974
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