Abstract
ABSTRACTConsider a multidimensional stochastic differential equation (SDE) driven by additive Lévy noises with one-sided Lipschitz continuous drift. By using the coupling method, we prove the regularity (including the Hölder continuity and the Lipschitz continuity) of the associated semigroups, under the assumption that the Lévy measure of the driving Lévy process satisfies for some non-negative measurable function ρ on . Our result efficiently applies to symmetric α-stable process driven SDEs, and also to the case that ρ is regularly varying at the origin with index or .
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