A Unified Approach to Coupling SDEs driven by Lévy Noise and Some Applications

Abstract

We present a general method to construct couplings of stochastic differential equations driven by Lévy noise in terms of coupling operators. This approach covers both coupling by reflection and refined basic coupling which are often discussed in the literature. As an application, we establish regularity results for the transition semigroups of the solutions to stochastic differential equations driven by additive Lévy noise.

arXiv comment21 pages

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Cited by in corpus (2)

• Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise
• Exponential ergodicity for general continuous-state nonlinear branching processes