Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling
arXiv:1610.06916 · doi:10.1214/18-AIHP941
Abstract
By using the mirror coupling for solutions of SDEs driven by pure jump Lévy processes, we extend some transportation and concentration inequalities, which were previously known only in the case where the coefficients in the equation satisfy a global dissipativity condition. Furthermore, by using the mirror coupling for the jump part and the coupling by reflection for the Brownian part, we extend analogous results for jump diffusions. To this end, we improve some previous results concerning such couplings and show how to combine the jump and the Brownian case. As a crucial step in our proof, we develop a novel method of bounding Malliavin derivatives of solutions of SDEs with both jump and Gaussian noise, which involves the coupling technique and which might be of independent interest. The bounds we obtain are new even in the case of diffusions without jumps.
40 pages, revised version, accepted for publication in Annales de l'Institut Henri Poincaré Probabilités et Statistiques. The final manuscript is available at Project Euclid via https://projecteuclid.org/euclid.aihp/1573203622
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