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Large deviation estimate of transition densities for jump processes. (English) Zbl 0877.60055
The author gives asymptotic upper and lower bounds of deviation type for the transition density of a jump type process on $$\mathbb R^d$$, which is composed of stable-like processes on the line and vector field on $$\mathbb R^d$$. To do this he uses the theory of Malliavin calculus both for diffusion and for jump type processes. In the case where there is no drift, the upper and lower bounds coincide.
Reviewer: J.H.Kim (Pusan)

##### MSC:
 60J75 Jump processes (MSC2010) 60J25 Continuous-time Markov processes on general state spaces 60F10 Large deviations
##### Keywords:
Jump processes; large deviation; transition density
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