Brownian and fractional Brownian stochastic currents via Malliavin calculus

DOI10.1016/j.jfa.2009.05.001zbMath1196.60100arXiv0907.0292OpenAlexW1968826539MaRDI QIDQ1048164

Franco Flandoli, Ciprian A. Tudor

Publication date: 11 January 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.0292

zbMATH Keywords

fractional Brownian motionBrownian motionMalliavin calculuscurrentsmultiple stochastic integrals

Mathematics Subject Classification ID

Gaussian processes (60G15) Brownian motion (60J65) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (7)

A white noise approach to stochastic currents of Brownian motion ⋮ An improved characterisation of regular generalised functions of white noise and an application to singular SPDEs ⋮ Solution existence for non-autonomous variable-order fractional differential equations ⋮ A shifted Jacobi-Gauss collocation scheme for solving fractional neutral functional-differential equations ⋮ 2D-stochastic currents over the Wiener sheet ⋮ New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions ⋮ Asymptotic behavior of stochastic currents under large deviation scaling with mean field interaction and vanishing noise

Cites Work

• Lectures on stochastic differential equations and Malliavin calculus
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• The central limit theorem for current-valued processes induced by geodesic flows
• Stochastic intersection number and homological behaviors of diffusion processes on Riemannian manifolds
• Large deviation for a class of current-valued processes
• Smoothness of Brownian local times and related functionals
• The asymptotic behaviour of local times and occupation integrals of the \(N\)-parameter Wiener process in \(\mathbb{R}^ d\)
• Tanaka formula for the fractional Brownian motion.
• Chaos expansions of double intersection local time of Brownian motion in \(\mathbb{R}^ d\) and renormalization
• Stochastic currents
• Sample path large deviations for a class of random currents.
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• Limit theorems for a class of diffusion processes
• Regularity of the Local Time for the d-dimensional Fractional Brownian Motion with N-parameters
• CHAOS EXPANSION OF LOCAL TIME OF FRACTIONAL BROWNIAN MOTIONS
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