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2007 Time Reversal for Drifted Fractional Brownian Motion with Hurst Index $H>1/2$
Sebastien Darses, Bruno Saussereau
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Electron. J. Probab. 12: 1181-1211 (2007). DOI: 10.1214/EJP.v12-439

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.

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Sebastien Darses. Bruno Saussereau. "Time Reversal for Drifted Fractional Brownian Motion with Hurst Index $H>1/2$." Electron. J. Probab. 12 1181 - 1211, 2007. https://doi.org/10.1214/EJP.v12-439

Information

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

zbMATH: 1130.60044
MathSciNet: MR2346508
Digital Object Identifier: 10.1214/EJP.v12-439

Subjects:
Primary: 60G18
Secondary: 60H07 , 60H10 , 60J60

Keywords: fractional Brownian motion , Malliavin calculus , Time reversal

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