A unified approach to coupling SDEs driven by Lévy noise and some applications (Q2278676)

In one of the first attempts to systematically treat coupling of jump processes which are not Lévy processes, the authors study Markovian couplings for stochastic differential equations (SDEs) driven by Lévy noise. Working with coupling operators, their approach of unifies the three known types of coupling, refined basic coupling, coupling by reflection, and coupling from the point of view optimal transport introduced by \textit{M. B. Majka} [Stochastic Processes Appl. 127, No. 12, 4083--4125 (2017; Zbl 1374.60088)]. The technique is applied to proving new regularity results for the transition semigroup and the couplings of the solutions of SDEs driven by additive Lévy noise. Optimality of the three couplings is discussed in a sense close to the notion of \textit{M. Chen} [Acta Math. Sin., New Ser. 10, No. 3, 260--275 (1994; Zbl 0813.60068)]. A possible extension to SDEs with multiplicative Lévy noise is also considered.