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Coupling property and gradient estimates of Lévy processes via the symbol. (English) Zbl 1263.60045

Based on the asymptotic behaviour of the symbol or the characteristic exponent near zero and infinity, respectively, the authors prove two main results: the coupling property for the transition semigroup of a Lévy process and gradient estimates for the associated semigroup of transition operators. Two examples are included to illustrate the optimality and the efficiency of these results.

MSC:

60G51 Processes with independent increments; Lévy processes
60J25 Continuous-time Markov processes on general state spaces
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