Derivative for self-intersection local time of multidimensional fractional Brownian motion

DOI10.1080/17442508.2015.1019883zbMath1337.60068OpenAlexW2152879397MaRDI QIDQ2804018

Xianye Yu, Litan Yan

Publication date: 27 April 2016

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442508.2015.1019883

zbMATH Keywords

fractional Brownian motionchaos expansionquadratic covariationself-intersection local timeoccupation formula

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Self-similar stochastic processes (60G18) (L^p)-limit theorems (60F25)

Related Items (13)

Existence and Hölder continuity conditions for self-intersection local time of Rosenblatt process ⋮ Derivative of intersection local time of independent symmetric stable motions ⋮ Unnamed Item ⋮ Smoothness of self-intersection local time of multidimensional fractional Brownian motion ⋮ Derivative for the intersection local time of two independent fractional Brownian motions ⋮ Higher-order derivative of self-intersection local time for fractional Brownian motion ⋮ Fractional smoothness of derivative of self-intersection local times ⋮ Self-intersection local time derivative for systems of non-linear stochastic heat equations ⋮ Smoothness of higher order derivative of self-intersection local time for fractional Brownian motion ⋮ Asymptotic properties for \(q\)-th chaotic component of derivative of self-intersection local time of fractional Brownian motion ⋮ Derivative of multiple self-intersection local time for fractional Brownian motion ⋮ Higher-order derivative of intersection local time for two independent fractional Brownian motions ⋮ Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion

Cites Work

• On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion
• Local time rough path for Lévy processes
• Local time and stochastic area integrals
• \(p\)-variation of an integral functional driven by fractional Brownian motion
• Integration with respect to fractional local time with Hurst index \(1/2 < \text H < 1\)
• The intersection local time of fractional Brownian motion in the plane
• Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index \(H\geq\frac 1 4\).
• Self-intersection local time of fractional Brownian motions -- via chaos expansion
• Renormalized self-intersection local time for fractional Brownian motion
• Integration with respect to local time
• 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
• Local time-space stochastic calculus for Lévy processes
• Two-parameter \(p,q\)-variation paths and integrations of local times
• Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter \(H \in (0,\frac {1}{2})\)
• A change-of-variable formula with local time on curves
• The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2
• The Malliavin Calculus and Related Topics

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