Small-time Behaviour of Lévy Processes

Ronald A. Doney (Department of Mathematics, University of Manchester, UK)


In this paper a necesary and sufficient condition is established for the probability that a Lévy process is positive at time $t$ to tend to 1 as $t$ tends to 0. This condition is expressed in terms of the characteristics of the process, and is also shown to be equivalent to two probabilistic statements about the behaviour of the process for small time $t$.

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Pages: 209--229

Publication Date: March 15, 2004

DOI: 10.1214/EJP.v9-193


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