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- Intersection local times of fractional Brownian motions with H∈(0,1) as generalized white noise functionalsPublication . Drumond, Custódia; Oliveira, Maria João; Silva, José Luís daIn R^d, for any dimension d ≥ 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.
- Intersection local times of independent fractional Brownian motions as generalized white noise functionalsPublication . Oliveira, Maria João; Silva, José Luís da; Streit, LudwigIn this work we present expansions of intersection local times of fractional Brownian motions in R^d , 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.