## Electronic Journal of Probability

### Harnack inequalities for SDEs driven by time-changed fractional Brownian motions

#### Abstract

We establish Harnack inequalities for stochastic differential equations (SDEs) driven by a time-changed fractional Brownian motion with Hurst parameter $H\in (0,1/2)$. The Harnack inequality is dimension-free if the SDE has a drift which satisfies a one-sided Lipschitz condition; otherwise we still get Harnack-type estimates, but the constants will, in general, depend on the space dimension. Our proof is based on a coupling argument and a regularization argument for the time-change.

#### Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 71, 23 pp.

Dates
Accepted: 11 July 2017
First available in Project Euclid: 13 September 2017

https://projecteuclid.org/euclid.ejp/1505268102

Digital Object Identifier
doi:10.1214/17-EJP82

Mathematical Reviews number (MathSciNet)
MR3698740

Zentralblatt MATH identifier
06797881

#### Citation

Deng, Chang-Song; Schilling, René L. Harnack inequalities for SDEs driven by time-changed fractional Brownian motions. Electron. J. Probab. 22 (2017), paper no. 71, 23 pp. doi:10.1214/17-EJP82. https://projecteuclid.org/euclid.ejp/1505268102

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