The fractional derivative for fractional Brownian local time with Hurst index large than 1/2

DOI10.1007/s00209-015-1606-5zbMath1338.60111OpenAlexW2212345685MaRDI QIDQ284812

Litan Yan

Publication date: 18 May 2016

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-015-1606-5

zbMATH Keywords

Cauchy principal valuefractional Brownian motionMalliavin calculuslocal timefractional derivative

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Fractional derivatives and integrals (26A33) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Local time and additive functionals (60J55)

Related Items (5)

Limit theorems related to the integral functionals of one dimensional fractional Brownian motion ⋮ Bismut type derivative formulae and gradient estimate for multiplicative SDEs with fractional noises ⋮ An integral functional driven by fractional Brownian motion ⋮ Forward and symmetric Wick-Itô integrals with respect to fractional Brownian motion ⋮ Derivative formulas and applications for degenerate stochastic differential equations with fractional noises

Cites Work

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• Selected aspects of fractional Brownian motion.
• On the fractional derivative of Brownian local times
• On the increments of the principal value of Brownian local time
• Aspects of Brownian motion
• Integration with respect to fractional local time with Hurst index \(1/2 < \text H < 1\)
• Occupation densities
• Limit theorems and variation properties for fractional derivatives of the local time of a stable process
• On the distribution of the Hilbert transform of the local time of a symmetric Lévy process
• Regularity of the Cauchy principal value of the local times of some Lévy processes
• Stochastic analysis of the fractional Brownian motion
• Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index \(H\geq\frac 1 4\).
• The laws of Chung and Hirsch for Cauchy's principal values related to Brownian local times
• Increment sizes of the principal value of Brownian local time
• Integration questions related to fractional Brownian motion
• Tanaka formula for the fractional Brownian motion.
• Chaotic expansion and smoothness of some functionals of the fractional Brownian motion
• Complements on the Hilbert transform and the fractional derivative of Brownian local times
• Stochastic calculus for fractional Brownian motion and related processes.
• \(m\)-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index
• The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2
• Integral transformations and anticipative calculus for fractional Brownian motions
• The Malliavin Calculus and Related Topics
• Weighted Local Time for Fractional Brownian Motion and Applications to Finance
• A joint functional law for the Wiener process and principal value
• Stochastic Calculus for Fractional Brownian Motion and Applications
• Stochastic calculus with respect to Gaussian processes

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