Coupling property and gradient estimates of Lévy processes via the symbol
We derive explicitly the coupling property for the transition semigroup of a Lévy process and gradient estimates for the associated semigroup of transition operators. This is based on the asymptotic behaviour of the symbol or the characteristic exponent near zero and infinity, respectively. Our resu...
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| Veröffentlicht in: | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2012-11, Vol.18 (4), p.1128-1149 |
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| container_title | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability |
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| creator | SCHILLING, RENÉ L. SZTONYK, PAWEŁ WANG, JIAN |
| description | We derive explicitly the coupling property for the transition semigroup of a Lévy process and gradient estimates for the associated semigroup of transition operators. This is based on the asymptotic behaviour of the symbol or the characteristic exponent near zero and infinity, respectively. Our results can be applied to a large class of Levy processes, including stable Levy processes, layered stable processes, tempered stable processes and relativistic stable processes. |
| doi_str_mv | 10.3150/11-bej375 |
| format | Article |
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| language | eng |
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| source | Jstor Complete Legacy; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | coupling Density Density estimation gradient estimates Infinity Lévy process Markov processes Mathematical theorems Mathematics Property titles Semigroups Stochastic processes symbol Symbols |
| title | Coupling property and gradient estimates of Lévy processes via the symbol |
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