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2006.50: Curve Crossing for the Reflected Process

2006.50: Ron Doney and Ross Maller (2006) Curve Crossing for the Reflected Process.

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Abstract

Let R_n = max0<=j<=n S_j − S_n be a random walk S_n reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times of Rn above horizontal or certain curved (power law) boundaries. Necessary and sufficient conditions are also given for the finiteness of the expected passage time of R_n above linear and square root boundaries.

Item Type:MIMS Preprint
Uncontrolled Keywords:Reflected process, rate of growth, renewal theorems, power law boundaries.
Subjects:MSC 2000 > 60 Probability theory and stochastic processes
MIMS number:2006.50
Deposited By:Dr Peter Neal
Deposited On:05 April 2006

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