Intersection local times of fractional Brownian motions with $H\in (0,1)$ as generalized white noise functionals

Abstract

In ${\mathbb{R}}^d$, for any dimension $d\ge 1$, expansions of self-intersection local times of fractional Brownian motions with arbitrary Hurst coefficients in $(0,1)$ are presented. 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.

17 pages

References in corpus (1)

• Renormalized self-intersection local time for fractional Brownian motion

Cited by in corpus (4)

• Mittag-Leffler Analysis I: Construction and characterization
• Intersection local times of independent fractional Brownian motions as generalized white noise functionals
• Local times for multifractional Brownian motion in higher dimensions: A white noise approach
• Generalized Fock space and moments