Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling

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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.

Original languageEnglish
Pages (from-to)2019-2057
Number of pages39
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume55
Issue number4
DOIs
Publication statusPublished - 8 Nov 2019

Keywords

  • Couplings
  • Lévy processes
  • Malliavin calculus
  • Stochastic differential equations
  • Transportation inequalities
  • Wasserstein distances

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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