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Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling
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Majka, Mateusz B. (2019) Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling. Annales de l'Institut Henri Poincare (B) Probability and Statistics, 55 (4). pp. 2019-2057. doi:10.1214/18-AIHP941 ISSN 0246-0203.
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Official URL: https://doi.org/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.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Stochastic differential equations, Lévy processes, Random noise theory | |||||||||
Journal or Publication Title: | Annales de l'Institut Henri Poincare (B) Probability and Statistics | |||||||||
Publisher: | Institute of Mathematical Statistics | |||||||||
ISSN: | 0246-0203 | |||||||||
Official Date: | November 2019 | |||||||||
Dates: |
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Volume: | 55 | |||||||||
Number: | 4 | |||||||||
Page Range: | pp. 2019-2057 | |||||||||
DOI: | 10.1214/18-AIHP941 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Copyright Holders: | Copyright © 2019 Institut Henri Poincaré | |||||||||
Date of first compliant deposit: | 18 December 2018 | |||||||||
Date of first compliant Open Access: | 18 December 2018 | |||||||||
RIOXX Funder/Project Grant: |
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