Displaying similar documents to “Lacunary Fractional Brownian Motion”

Lacunary Fractional Brownian Motion

Marianne Clausel (2012)

ESAIM: Probability and Statistics

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In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Multifractional brownian fields indexed by metric spaces with distances of negative type

Jacques Istas (2013)

ESAIM: Probability and Statistics

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We define multifractional Brownian fields indexed by a metric space, such as a manifold with its geodesic distance, when the distance is of negative type. This construction applies when the Brownian field indexed by the metric space exists, in particular for spheres, hyperbolic spaces and real trees.

Differential equations driven by fractional Brownian motion.

David Nualart, Aurel Rascanu (2002)

Collectanea Mathematica

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A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

A Milstein-type scheme without Lévy area terms for SDEs driven by fractional brownian motion

A. Deya, A. Neuenkirch, S. Tindel (2012)

Annales de l'I.H.P. Probabilités et statistiques

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In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second-order Taylor expansion, where the usual Lévy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error...

Probabilistic models for vortex filaments based on fractional brownian motion.

David Nualart, Carles Rovira, Samy Tindel (2001)

RACSAM

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Se introduce una estructura de vorticidad basada en el movimiento browniano fraccionario con parámetro de Hurst H > 1/2 . El objeto de esta nota es presentar el siguiente resultado: Bajo una condición de integrabilidad adecuada sobre la medida ρ que controla la concentración de la vorticidad a lo largo de los filamentos, la energía cinética de la configuración está bien definida y tiene momentos de todos los órdenes.