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Logarithmic Sobolev inequalities for fractional diffusion

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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