Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Strong Feller properties for degenerate SDEs with jumps

Zhao Dong, Xuhui Peng, Yulin Song, and Xicheng Zhang

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Abstract

Under full Hörmander’s conditions, we prove the strong Feller property of the semigroup determined by an SDE driven by additive subordinate Brownian motions, where the drift is allowed to be arbitrary growth. For this, we extend a criterion due to Malicet and Poly (J. Funct. Anal. 264 (2013) 2077–2096) and Bally and Caramellino (Electron. J. Probab. 19 (2014) 1–33) about the convergence of the laws of Wiener functionals in total variation. Moreover, the example of a chain of coupled oscillators is verified.

Résumé

Sous des conditions de Hörmander fortes, nous prouvons la propriété forte de Feller pour le semi-groupe déterminé par une SDE dirigée par des mouvements browniens subordonnés additifs, où la dérive est autorisée à être arbitrairement croissante. Pour cela, nous étendons un critère dû à Malicet et Poly (J. Funct. Anal. 264 (2013) 2077–2096) et à Bally et Caramellino (Electron. J. Probab. 19 (2014) 1–33) sur la convergence, en variation totale, des lois de fonctionnelles de Wiener. Ce résultat couvre le cas d’une chaîne d’oscillateurs couplés.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 52, Number 2 (2016), 888-897.

Dates
Received: 12 February 2014
Revised: 20 October 2014
Accepted: 23 October 2014
First available in Project Euclid: 4 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1462367898

Digital Object Identifier
doi:10.1214/14-AIHP658

Mathematical Reviews number (MathSciNet)
MR3498014

Zentralblatt MATH identifier
1346.60080

Keywords
Strong Feller property SDE Malliavin’s calculus Cylindrical $\alpha$-stable process Hörmander’s condition

Citation

Dong, Zhao; Peng, Xuhui; Song, Yulin; Zhang, Xicheng. Strong Feller properties for degenerate SDEs with jumps. Ann. Inst. H. Poincaré Probab. Statist. 52 (2016), no. 2, 888--897. doi:10.1214/14-AIHP658. https://projecteuclid.org/euclid.aihp/1462367898


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