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On smoothing properties of transition semigroups associated to a class of SDEs with jumps

Seiichiro Kusuoka; Carlo Marinelli — 2014

Annales de l'I.H.P. Probabilités et statistiques

We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) in $ℝ^{d}$ driven by additive pure-jump Lévy noise. In particular, we assume that the Lévy process driving the SDE is the sum of a subordinated Wiener process $Y$ (i.e. $Y = W \circ T$ , where $T$ is an increasing pure-jump Lévy process starting at zero and independent of the Wiener process $W$ ) and of an arbitrary Lévy process independent of $Y$ , that the drift coefficient is continuous (but not...

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