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2008 Curve Crossing for the Reflected Levy Process at Zero and Infinity
Mladen Savov
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Electron. J. Probab. 13: 157-172 (2008). DOI: 10.1214/EJP.v13-483


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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Mladen Savov. "Curve Crossing for the Reflected Levy Process at Zero and Infinity." Electron. J. Probab. 13 157 - 172, 2008.


Accepted: 30 January 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60037
MathSciNet: MR2375603
Digital Object Identifier: 10.1214/EJP.v13-483

Primary: 60G51
Secondary: 60F15 , 60G40 , 60G44 , 60K05

Keywords: passage times , power law boundaries , reflected process

Vol.13 • 2008
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