Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump

Ouyang S-X, Röckner M, Wang F-Y (2012)
Potential Analysis 36(2): 301-315.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
The Harnack inequality established in Rockner and Wang (J Funct Anal 203:237-261, 2003) for generalized Mehler semigroup is improved and generalized. As applications, the log-Harnack inequality, the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroups with jump. These inequalities and semigroup properties are indeed equivalent, and thus sharp, for the Gaussian case. As an application of the log-Harnack inequality, the HWI inequality is established for the Gaussian case. Perturbations with linear growth are also investigated.
Stichworte
Ornstein-Uhlenbeck process; Harnack inequality; Entropy-cost inequality; Levy process
Erscheinungsjahr
2012
Zeitschriftentitel
Potential Analysis
Band
36
Ausgabe
2
Seite(n)
301-315
ISSN
0926-2601
Page URI
https://pub.uni-bielefeld.de/record/2474345

Zitieren

Ouyang S-X, Röckner M, Wang F-Y. Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump. Potential Analysis. 2012;36(2):301-315.
Ouyang, S. - X., Röckner, M., & Wang, F. - Y. (2012). Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump. Potential Analysis, 36(2), 301-315. doi:10.1007/s11118-011-9231-3
Ouyang, S. - X., Röckner, M., and Wang, F. - Y. (2012). Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump. Potential Analysis 36, 301-315.
Ouyang, S.-X., Röckner, M., & Wang, F.-Y., 2012. Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump. Potential Analysis, 36(2), p 301-315.
S.-X. Ouyang, M. Röckner, and F.-Y. Wang, “Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump”, Potential Analysis, vol. 36, 2012, pp. 301-315.
Ouyang, S.-X., Röckner, M., Wang, F.-Y.: Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump. Potential Analysis. 36, 301-315 (2012).
Ouyang, Shun-Xiang, Röckner, Michael, and Wang, Feng-Yu. “Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump”. Potential Analysis 36.2 (2012): 301-315.