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

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

2010-01-04

arxiv.org/abs/1001.0513v1

Acta Appl. Math. 113 (1) (2011), 17-39

Mathematics

Probability

28 pages

Scientific paper

10.1007/s10440-010-9579-1

In this work we present expansions of intersection local times of fractional Brownian motions in $\R^d$, for any dimension $d\geq 1$, 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.

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