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 Electronic Communications in Probability > Vol. 14 (2009) > Paper 13 open journal systems 


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 ≥ 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.


Full text: PDF

Pages: 132-142

Published on: March 1, 2009
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Electronic Communications in Probability. ISSN: 1083-589X