Open Access
2017 Harnack inequalities for SDEs driven by time-changed fractional Brownian motions
Chang-Song Deng, René L. Schilling
Electron. J. Probab. 22: 1-23 (2017). DOI: 10.1214/17-EJP82


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.


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Chang-Song Deng. René L. Schilling. "Harnack inequalities for SDEs driven by time-changed fractional Brownian motions." Electron. J. Probab. 22 1 - 23, 2017.


Received: 4 September 2016; Accepted: 11 July 2017; Published: 2017
First available in Project Euclid: 13 September 2017

zbMATH: 06797881
MathSciNet: MR3698740
Digital Object Identifier: 10.1214/17-EJP82

Primary: 60G15 , 60G22 , 60H10

Keywords: fractional Brownian motion , Harnack inequality , random time-change , Stochastic differential equation

Vol.22 • 2017
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