## Electronic Journal of Probability

### Time Reversal for Drifted Fractional Brownian Motion with Hurst Index $H>1/2$

#### Abstract

Let $X$ be a drifted fractional Brownian motion with Hurst index $H > 1/2$. We prove that there exists a fractional backward representation of $X$, i.e. the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when $H=1/2$. We then apply our result to stochastic differential equations driven by a fractional Brownian motion.

#### Article information

Source
Electron. J. Probab., Volume 12 (2007), paper no. 43, 1181-1211.

Dates
Accepted: 7 September 2007
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464818514

Digital Object Identifier
doi:10.1214/EJP.v12-439

Mathematical Reviews number (MathSciNet)
MR2346508

Zentralblatt MATH identifier
1130.60044

Rights

#### Citation

Darses, Sebastien; Saussereau, Bruno. Time Reversal for Drifted Fractional Brownian Motion with Hurst Index $H&gt;1/2$. Electron. J. Probab. 12 (2007), paper no. 43, 1181--1211. doi:10.1214/EJP.v12-439. https://projecteuclid.org/euclid.ejp/1464818514

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