IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i9p1436-1444.html
   My bibliography  Save this article

Harnack inequalities for Ornstein-Uhlenbeck processes driven by Lévy processes

Author

Listed:
  • Wang, Jian

Abstract

By using the existing sharp estimates of the density function for rotationally invariant symmetric [alpha]-stable Lévy processes and rotationally invariant symmetric truncated [alpha]-stable Lévy processes, we obtain that the Harnack inequalities hold for rotationally invariant symmetric [alpha]-stable Lévy processes with [alpha][set membership, variant](0,2) and Ornstein-Uhlenbeck processes driven by rotationally invariant symmetric [alpha]-stable Lévy process, while the logarithmic Harnack inequalities are satisfied for rotationally invariant symmetric truncated [alpha]-stable Lévy processes.

Suggested Citation

  • Wang, Jian, 2011. "Harnack inequalities for Ornstein-Uhlenbeck processes driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1436-1444, September.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:9:p:1436-1444
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211001593
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    2. Wang, Feng-Yu, 2011. "Gradient estimate for Ornstein-Uhlenbeck jump processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 466-478, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Böttcher, Björn & Schilling, René L. & Wang, Jian, 2011. "Constructions of coupling processes for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1201-1216, June.
    2. Peng Jin, 2021. "Uniqueness in Law for Stable-Like Processes of Variable Order," Journal of Theoretical Probability, Springer, vol. 34(2), pages 522-552, June.
    3. Kim, Panki, 2006. "Weak convergence of censored and reflected stable processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1792-1814, December.
    4. Weidner, Marvin, 2023. "Markov chain approximations for nonsymmetric processes," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 238-281.
    5. Paweł Sztonyk, 2010. "Estimates of Tempered Stable Densities," Journal of Theoretical Probability, Springer, vol. 23(1), pages 127-147, March.
    6. Sztonyk, Pawel, 2011. "Transition density estimates for jump Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1245-1265, June.
    7. Feng-Yu Wang & Jian Wang, 2015. "Functional Inequalities for Stable-Like Dirichlet Forms," Journal of Theoretical Probability, Springer, vol. 28(2), pages 423-448, June.
    8. Haruna Okamura & Toshihiro Uemura, 2021. "On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities," Journal of Theoretical Probability, Springer, vol. 34(2), pages 809-826, June.
    9. Yulin Song, 2020. "Gradient Estimates and Exponential Ergodicity for Mean-Field SDEs with Jumps," Journal of Theoretical Probability, Springer, vol. 33(1), pages 201-238, March.
    10. Kaleta, Kamil & Pietruska-Pałuba, Katarzyna, 2015. "Integrated density of states for Poisson–Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1244-1281.
    11. Viktorya Knopova & René L. Schilling, 2012. "Transition Density Estimates for a Class of Lévy and Lévy-Type Processes," Journal of Theoretical Probability, Springer, vol. 25(1), pages 144-170, March.
    12. Wang, Linlin & Xie, Longjie & Zhang, Xicheng, 2015. "Derivative formulae for SDEs driven by multiplicative α-stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 867-885.
    13. Wang, Feng-Yu & Wang, Jian, 2013. "Coupling and strong Feller for jump processes on Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1588-1615.
    14. Chen, Xin & Chen, Zhen-Qing & Wang, Jian, 2020. "Heat kernel for non-local operators with variable order," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3574-3647.
    15. Chen, Zhen-Qing & Hu, Eryan, 2015. "Heat kernel estimates for Δ+Δα/2 under gradient perturbation," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2603-2642.
    16. Kim, Panki & Song, Renming & Vondraček, Zoran, 2013. "Potential theory of subordinate Brownian motions with Gaussian components," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 764-795.
    17. Kaleta, Kamil & Pietruska-Pałuba, Katarzyna, 2018. "Lifschitz singularity for subordinate Brownian motions in presence of the Poissonian potential on the Sierpiński gasket," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3897-3939.
    18. Ante Mimica, 2013. "Harnack Inequality and Hölder Regularity Estimates for a Lévy Process with Small Jumps of High Intensity," Journal of Theoretical Probability, Springer, vol. 26(2), pages 329-348, June.
    19. Jacob, Niels & Potrykus, Alexander & Wu, Jiang-Lun, 2010. "Solving a non-linear stochastic pseudo-differential equation of Burgers type," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2447-2467, December.
    20. Xie, Longjie, 2017. "Singular SDEs with critical non-local and non-symmetric Lévy type generator," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3792-3824.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:9:p:1436-1444. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.