Electronic Journal of Probability

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

Sebastien Darses and Bruno Saussereau

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G18: Self-similar processes
Secondary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60: Diffusion processes [See also 58J65]

Fractional Brownian motion Time reversal Malliavin Calculus

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Darses, Sebastien; Saussereau, Bruno. Time Reversal for Drifted Fractional Brownian Motion with Hurst Index $H>1/2$. 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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