Curve crossing for the reflected Levy process at zero and infinitySavov, S. S. (2008) Curve crossing for the reflected Levy process at zero and infinity. Electronic Journal of Probability, 13. pp. 157-172. ISSN 1083-6489 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1214/EJP.v13-483 Abstract/SummaryLet $R_{t}=\sup_{0\leq s\leq t}X_{s}-X_{t}$ 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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