Renewal theorems and stability for the reflected process

Ron Doney, Ross Maller and Mladen Savov

Stochastic Processes and their Applications, 2009, vol. 119, issue 4, 1270-1297

Abstract: Renewal-like results and stability theorems relating to the large-time behaviour of a random walk Sn reflected in its maximum, Rn=max0 [infinity]ER[tau](r)/r=1 is shown to hold when EX [infinity] and limr-->[infinity]R[tau](r)/r=1 almost surely (a.s.); alternatively expressed, the overshoot R[tau](r)-r is o(r) as r-->[infinity], in probability or a.s. Comparisons are also made with exit times of the random walk Sn across both two-sided and one-sided horizontal boundaries.

Keywords: Reflected; process; Passage; times; Renewal; theorems; Overshoot (search for similar items in EconPapers)
Date: 2009
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