Volume 30, Issue 1
Harnack Inequality and Applications for Stochastic Retarded Differential Equations Driven by Fractional Brownian Motion

Min Liu, Liping Xu, Zhi Li & Zhong Chen

J. Part. Diff. Eq., 30 (2017), pp. 84-94.

Published online: 2017-03

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  • Abstract

In this paper, by using a semimartingale approximation of a fractional stochastic integration, the global Harnack inequalities for stochastic retarded differential equations driven by fractional Brownian motion with Hurst parameter 0 ‹ H ‹ 1 are established. As applications, strong Feller property, log-Harnack inequality and entropycost inequality are given.

  • Keywords

Fractional Brownian motion Harnack inequality strong Feller property

  • AMS Subject Headings

60G15, 60H05, 60H15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

fqbu@yangtzeu.edu.cn (Min Liu)

xlp211@126.com (Liping Xu)

lizhi_csu@126.com (Zhi Li)

czhong@yangtzeu.edu.cn (Zhong Chen)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-30-84, author = {Liu , Min and Xu , Liping and Li , Zhi and Chen , Zhong }, title = {Harnack Inequality and Applications for Stochastic Retarded Differential Equations Driven by Fractional Brownian Motion}, journal = {Journal of Partial Differential Equations}, year = {2017}, volume = {30}, number = {1}, pages = {84--94}, abstract = { In this paper, by using a semimartingale approximation of a fractional stochastic integration, the global Harnack inequalities for stochastic retarded differential equations driven by fractional Brownian motion with Hurst parameter 0 ‹ H ‹ 1 are established. As applications, strong Feller property, log-Harnack inequality and entropycost inequality are given.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v30.n1.7}, url = {http://global-sci.org/intro/article_detail/jpde/5073.html} }
TY - JOUR T1 - Harnack Inequality and Applications for Stochastic Retarded Differential Equations Driven by Fractional Brownian Motion AU - Liu , Min AU - Xu , Liping AU - Li , Zhi AU - Chen , Zhong JO - Journal of Partial Differential Equations VL - 1 SP - 84 EP - 94 PY - 2017 DA - 2017/03 SN - 30 DO - http://doi.org/10.4208/jpde.v30.n1.7 UR - https://global-sci.org/intro/article_detail/jpde/5073.html KW - Fractional Brownian motion KW - Harnack inequality KW - strong Feller property AB - In this paper, by using a semimartingale approximation of a fractional stochastic integration, the global Harnack inequalities for stochastic retarded differential equations driven by fractional Brownian motion with Hurst parameter 0 ‹ H ‹ 1 are established. As applications, strong Feller property, log-Harnack inequality and entropycost inequality are given.
Min Liu, Liping Xu, Zhi Li & Zhong Chen. (2019). Harnack Inequality and Applications for Stochastic Retarded Differential Equations Driven by Fractional Brownian Motion. Journal of Partial Differential Equations. 30 (1). 84-94. doi:10.4208/jpde.v30.n1.7
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