An extension of the Lévy characterization to fractional Brownian motion

DOI10.1214/10-AOP555zbMath1227.60051arXivmath/0611913OpenAlexW3102244812MaRDI QIDQ2431515

Esko Valkeila, Yuliya S. Mishura

Publication date: 15 April 2011

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611913

zbMATH Keywords

fractional Brownian motionmartingalesLévy theorem

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Stochastic analysis (60H99)

Related Items (6)

On integration by parts formula and characterization of fractional Ornstein-Uhlenbeck process ⋮ Large deviations of Shepp statistics for fractional Brownian motion ⋮ Optimal Sequential Change Detection for Fractional Diffusion-Type Processes ⋮ On Piterbarg's max-discretisation theorem for multivariate stationary Gaussian processes ⋮ Fractional martingales and characterization of the fractional Brownian motion ⋮ Integration with respect to fractional local time with Hurst index \(1/2 < \text H < 1\)

Cites Work

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• Fractional martingales and characterization of the fractional Brownian motion
• An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
• Stochastic calculus for fractional Brownian motion and related processes.
• L\({}^ p\) estimates on iterated stochastic integrals
• Arbitrage with Fractional Brownian Motion
• Linear Problems for a Fractional Brownian Motion: Group Approach
• Fractional Brownian Motions, Fractional Noises and Applications

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