IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v106y2015icp165-172.html
   My bibliography  Save this article

Logarithmic Sobolev inequalities for fractional diffusion

Author

Listed:
  • Fan, XiLiang

Abstract

In this note, logarithmic Sobolev inequalities are established on the path space for the fractional Brownian motion with drift. The reference distance on the path space is the L2-norm of the gradient along paths.

Suggested Citation

  • Fan, XiLiang, 2015. "Logarithmic Sobolev inequalities for fractional diffusion," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 165-172.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:165-172
    DOI: 10.1016/j.spl.2015.07.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521500262X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.07.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Baudoin, Fabrice & Ouyang, Cheng, 2011. "Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 759-792, April.
    2. Nualart, David & Saussereau, Bruno, 2009. "Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 391-409, February.
    3. Nourdin, Ivan & Simon, Thomas, 2006. "On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 907-912, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiliang Fan, 2019. "Derivative Formulas and Applications for Degenerate Stochastic Differential Equations with Fractional Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1360-1381, September.

    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. Xiliang Fan, 2019. "Derivative Formulas and Applications for Degenerate Stochastic Differential Equations with Fractional Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1360-1381, September.
    2. Yamada, Toshihiro, 2015. "A formula of small time expansion for Young SDE driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 64-72.
    3. Shevchenko, Georgiy & Shalaiko, Taras, 2013. "Malliavin regularity of solutions to mixed stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2638-2646.
    4. Nourdin, Ivan & Peccati, Giovanni & Viens, Frederi G., 2014. "Comparison inequalities on Wiener space," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1566-1581.
    5. Eric Djeutcha & Didier Alain Njamen Njomen & Louis-Aimé Fono, 2019. "Solving Arbitrage Problem on the Financial Market Under the Mixed Fractional Brownian Motion With Hurst Parameter H ∈]1/2,3/4[," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(1), pages 76-92, February.
    6. Baudoin, Fabrice & Ouyang, Cheng & Zhang, Xuejing, 2015. "Varadhan estimates for rough differential equations driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 634-652.
    7. Quer-Sardanyons, Lluís & Tindel, Samy, 2012. "Pathwise definition of second-order SDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 466-497.
    8. Bondarenko, Valeria & Bondarenko, Victor & Truskovskyi, Kyryl, 2017. "Forecasting of time data with using fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 44-50.
    9. Andreas Neuenkirch & Ivan Nourdin, 2007. "Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 20(4), pages 871-899, December.
    10. Yaozhong Hu & Samy Tindel, 2013. "Smooth Density for Some Nilpotent Rough Differential Equations," Journal of Theoretical Probability, Springer, vol. 26(3), pages 722-749, September.
    11. Sin, Myong-Guk & Ri, Kyong-Il & Kim, Kyong-Hui, 2022. "Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 190(C).
    12. Boufoussi, Brahim & Hajji, Salah, 2012. "Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1549-1558.
    13. Peter Kloeden & Andreas Neuenkirch & Raffaella Pavani, 2011. "Multilevel Monte Carlo for stochastic differential equations with additive fractional noise," Annals of Operations Research, Springer, vol. 189(1), pages 255-276, September.
    14. Fan, Xiliang & Yu, Ting & Yuan, Chenggui, 2023. "Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 383-415.
    15. Baudoin, Fabrice & Ouyang, Cheng, 2011. "Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 759-792, April.
    16. Akahori, Jiro & Song, Xiaoming & Wang, Tai-Ho, 2019. "Bridge representation and modal-path approximation," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 174-204.
    17. Nualart, David & Saussereau, Bruno, 2009. "Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 391-409, February.
    18. Jorge A. León & Samy Tindel, 2012. "Malliavin Calculus for Fractional Delay Equations," Journal of Theoretical Probability, Springer, vol. 25(3), pages 854-889, September.
    19. Benjamin Gess & Cheng Ouyang & Samy Tindel, 2020. "Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths," Journal of Theoretical Probability, Springer, vol. 33(2), pages 611-648, June.
    20. Alexandra Chronopoulou & Samy Tindel, 2013. "On inference for fractional differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 29-61, April.

    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:106:y:2015:i:c:p:165-172. 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.