Strong Feller properties for degenerate SDEs with jumps

Zhao Dong; Xuhui Peng; Yulin Song; Xicheng Zhang

doi:10.1214/14-AIHP658

Strong Feller properties for degenerate SDEs with jumps

Zhao Dong, Xuhui Peng^*, Yulin Song, Xicheng Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	888-897
Number of pages	10
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	52
Issue number	2
DOIs	https://doi.org/10.1214/14-AIHP658
Publication status	Published - May 2016
Externally published	Yes

Keywords

Cylindrical α-stable process
Hörmander's condition
Malliavin's calculus
SDE
Strong Feller property

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10.1214/14-AIHP658

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title = "Strong Feller properties for degenerate SDEs with jumps",

abstract = "Under full H{\"o}rmander'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.",

keywords = "Cylindrical α-stable process, H{\"o}rmander's condition, Malliavin's calculus, SDE, Strong Feller property",

author = "Zhao Dong and Xuhui Peng and Yulin Song and Xicheng Zhang",

note = "Publisher Copyright: {\textcopyright} Association des Publications de l'Institut Henri Poincar{\'e}, 2016.",

year = "2016",

month = may,

doi = "10.1214/14-AIHP658",

language = "English",

volume = "52",

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journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",

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T1 - Strong Feller properties for degenerate SDEs with jumps

AU - Dong, Zhao

AU - Peng, Xuhui

AU - Song, Yulin

AU - Zhang, Xicheng

N1 - Publisher Copyright: © Association des Publications de l'Institut Henri Poincaré, 2016.

PY - 2016/5

Y1 - 2016/5

N2 - 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.

AB - 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.

KW - Cylindrical α-stable process

KW - Hörmander's condition

KW - Malliavin's calculus

KW - SDE

KW - Strong Feller property

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U2 - 10.1214/14-AIHP658

DO - 10.1214/14-AIHP658

M3 - Article

AN - SCOPUS:84973293649

SN - 0246-0203

VL - 52

SP - 888

EP - 897

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 2

ER -

Strong Feller properties for degenerate SDEs with jumps

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Keywords

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