Abstract
In this work we present expansions of intersection local times of fractional Brownian motions in ℝd, for any dimension d≥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 in Nualart and Ortiz-Latorre (J. Theoret. Probab. 20(4):759–767, 2007) to different and more general Hurst coefficients.
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Oliveira, M.J., da Silva, J.L. & Streit, L. Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals. Acta Appl Math 113, 17–39 (2011). https://doi.org/10.1007/s10440-010-9579-1
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DOI: https://doi.org/10.1007/s10440-010-9579-1