Intersection local time for two independent fractional Brownian motions

DOI10.1007/s10959-007-0106-xzbMath1154.60028arXiv0704.1259OpenAlexW2063256206MaRDI QIDQ2471118

David Nualart, Salvador Ortiz-Latorre

Publication date: 18 February 2008

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

Full work available at URL: https://arxiv.org/abs/0704.1259

zbMATH Keywords

fractional Brownian motionintersection local time

Mathematics Subject Classification ID

Gaussian processes (60G15) Self-similar stochastic processes (60G18) Local time and additive functionals (60J55) (L^p)-limit theorems (60F25)

Related Items (22)

A first-order limit law for functionals of two independent fractional Brownian motions in the critical case ⋮ Smoothness of self-intersection local time of multidimensional fractional Brownian motion ⋮ Derivative for the intersection local time of two independent fractional Brownian motions ⋮ Regularity of intersection local times of fractional Brownian motions ⋮ Intersection local times of independent fractional Brownian motions as generalized white noise functionals ⋮ Central limit theorem for functionals of two independent fractional Brownian motions ⋮ On the self-intersection local time of subfractional Brownian motion ⋮ Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes ⋮ Some properties of the Itô-Wiener expansion of the solution of a stochastic differential equation and local times ⋮ Self-avoiding fractional Brownian motion -- the Edwards model ⋮ Smoothness for the collision local time of two multidimensional bifractional Brownian motions ⋮ Derivatives of local times for some Gaussian fields. II ⋮ Collision local times of two independent fractional Brownian motions ⋮ Limit theorems for functionals of two independent Gaussian processes ⋮ Remarks on the intersection local time of fractional Brownian motions ⋮ Asymptotic behavior for an additive functional of two independent self-similar Gaussian processes ⋮ Derivatives of local times for some Gaussian fields ⋮ ON THE COLLISION LOCAL TIME OF BIFRACTIONAL BROWNIAN MOTIONS ⋮ Higher-order derivative of intersection local time for two independent fractional Brownian motions ⋮ Fractional Brownian sheets run with nonlinear clocks ⋮ Mixed fractional Brownian sheets and their applications ⋮ Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion

Cites Work

• A local time analysis of intersections of Brownian paths in the plane
• The intersection local time of fractional Brownian motion in the plane
• Local time and a particle picture for Euclidean field theory
• Wiener path intersections and local time
• Probabilistic models for vortex filaments based on fractional Brownian motion.
• Additive functionals of several Lévy processes and intersection local times
• Renormalized self-intersection local time for fractional Brownian motion
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