Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Transportation inequalities for stochastic differential equations of pure jumps

Liming Wu

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Abstract

For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that W1H transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the L1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given.

Résumé

Pour une équation différentielle stochastique de pur saut, bien que l’inégalité de Poincaré ne soit pas valide en général, nous pouvons quand même établir, sous la condition de dissipativité, des inégalités de transport W1H pour sa mesure invariante et pour sa loi (au niveau de processus) sur l’espace des trajectoires càdlàg, muni de la métrique L1 ou d’une métrique uniforme. Quelques applications aux inégalités de concentration sont présentées.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 46, Number 2 (2010), 465-479.

Dates
First available in Project Euclid: 11 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1273584131

Digital Object Identifier
doi:10.1214/09-AIHP320

Mathematical Reviews number (MathSciNet)
MR2667706

Zentralblatt MATH identifier
1209.60015

Subjects
Primary: 60E15: Inequalities; stochastic orderings 60H10: Stochastic ordinary differential equations [See also 34F05] 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
Transportation inequalities Stochastic differential equations Malliavin calculus

Citation

Wu, Liming. Transportation inequalities for stochastic differential equations of pure jumps. Ann. Inst. H. Poincaré Probab. Statist. 46 (2010), no. 2, 465--479. doi:10.1214/09-AIHP320. https://projecteuclid.org/euclid.aihp/1273584131


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