Small time expansions for transition probabilities of some Lévy processes

Philippe Marchal (CNRS and DMA, Ecole Normale Supérieure)

Abstract


We show that there exist Lévy processes $(X_t,t \geq 0)$ and reals $y>0$ such that for small $t$, the probability $P(X_t> y)$ has an expansion involving fractional powers or more general functions of $t$. This constrasts with previous results giving polynomial expansions under additional assumptions.

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Pages: 132-142

Publication Date: March 1, 2009

DOI: 10.1214/ECP.v14-1452

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