Intersection local times of independent fractional Brownian motions as generalized white noise functionals

Abstract

In this work we present expansions of intersection local times of fractional Brownian motions in ${\mathbb{R}}^d$, for any dimension $d\ge 1$, with arbitrary Hurst coefficients in $(0,1{)}^d$. The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals. As an application of our approach, a sufficient condition on $d$ for the existence of intersection local times in $L^2$ is derived, extending the results of D. Nualart and S. Ortiz-Latorre in "Intersection Local Time for Two Independent Fractional Brownian Motions" (J. Theoret. Probab.,20(4)(2007), 759-767) to different and more general Hurst coefficients.

28 pages

References in corpus (2)

• Renormalized self-intersection local time for fractional Brownian motion
• Intersection local times of fractional Brownian motions with $H\in (0,1)$ as generalized white noise functionals

Cited by in corpus (6)

• Mittag-Leffler Analysis I: Construction and characterization
• Self-avoiding fractional Brownian motion - The Edwards model
• Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion
• Higher-order derivative of intersection local time for two independent fractional Brownian motions
• Limit theorems for functionals of two independent Gaussian processes
• Brownian and fractional polymers with self-repulsion