Curve Crossing for the Reflected Levy Process at Zero and Infinity

Mladen Svetoslavov Savov (The University of Manchester)

Abstract


Let $R_{t}=\sup_{0\leq s\leq t}X_{s}-X_{t}$ be a Levy process reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times above power law boundaries at infinity. Information as to when the expected passage time for $R_{t}$ is finite, is given. We also discuss the almost sure finiteness of $\limsup_{t\to 0}R_{t}/t^{\kappa}$, for each $\kappa\geq 0$.

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Pages: 157-172

Publication Date: January 30, 2008

DOI: 10.1214/EJP.v13-483

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