Intersection local times of independent fractional Brownian motions as generalized white noise functionals
In 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...
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| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2012
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| Assuntos: | |
| Texto completo: | http://hdl.handle.net/10400.2/2033 |
| País: | Portugal |
| Oai: | oai:repositorioaberto.uab.pt:10400.2/2033 |
| Resumo: | In 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. |
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