Hölder continuity and occupation-time formulas for fBm self-intersection local time and its derivative

DOI10.1007/s10959-012-0474-8zbMath1432.60077arXiv1208.4407OpenAlexW2001441561MaRDI QIDQ2346982

Greg Markowsky, Paul H. Jung

Publication date: 26 May 2015

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.4407

zbMATH Keywords

fractional Brownian motionintersection local timeoccupation-time formula

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Local time and additive functionals (60J55)

Related Items (16)

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 ⋮ Existence and smoothness of local time and self-intersection local time for spherical Gaussian random fields ⋮ On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion ⋮ 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 ⋮ Renormalized self-intersection local time of bifractional 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

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• On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion
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• Local time and stochastic area integrals
• \(p\)-variation of an integral functional driven by fractional Brownian motion
• Renormalization and convergence in law for the derivative of intersection local time in \(\mathbf R^2\)
• 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
• Self-intersection gauge for random walks and for Brownian motion
• Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields
• Self-intersection local time of fractional Brownian motions -- via chaos expansion
• Renormalized self-intersection local time for fractional Brownian motion
• Limit laws for the intersection local time of stable processes in u²

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