The Annals of Probability

An extension of the Lévy characterization to fractional Brownian motion

Yuliya Mishura and Esko Valkeila

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Assume that X is a continuous square integrable process with zero mean, defined on some probability space (Ω, F, P). The classical characterization due to P. Lévy says that X is a Brownian motion if and only if X and Xt2t, t ≥ 0, are martingales with respect to the intrinsic filtration FX. We extend this result to fractional Brownian motion.

Article information

Ann. Probab. Volume 39, Number 2 (2011), 439-470.

First available in Project Euclid: 25 February 2011

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Mathematical Reviews number (MathSciNet)

Primary: 60G15: Gaussian processes
Secondary: 60E05: Distributions: general theory 60H99: None of the above, but in this section

Fractional Brownian motion Lévy theorem


Mishura, Yuliya; Valkeila, Esko. An extension of the Lévy characterization to fractional Brownian motion. Ann. Probab. 39 (2011), no. 2, 439--470. doi:10.1214/10-AOP555.

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