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Small time expansions for transition probabilities of some Lévy processes. (English) Zbl 1192.60071

Summary: 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.

MSC:

60G51 Processes with independent increments; Lévy processes
60J35 Transition functions, generators and resolvents
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