Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals

Oliveira MJ, da Silva JL, Streit L (2011)
Acta Applicandae Mathematicae 113(1): 17-39.

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In this work we present expansions of intersection local times of fractional Brownian motions in a"e (d) , for any dimension da parts per thousand yen1, 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 MJ, da Silva JL, Streit L. Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals. Acta Applicandae Mathematicae. 2011;113(1):17-39.
Oliveira, M. J., da Silva, J. L., & Streit, L. (2011). Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals. Acta Applicandae Mathematicae, 113(1), 17-39.
Oliveira, M. J., da Silva, J. L., and Streit, L. (2011). Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals. Acta Applicandae Mathematicae 113, 17-39.
Oliveira, M.J., da Silva, J.L., & Streit, L., 2011. Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals. Acta Applicandae Mathematicae, 113(1), p 17-39.
M.J. Oliveira, J.L. da Silva, and L. Streit, “Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals”, Acta Applicandae Mathematicae, vol. 113, 2011, pp. 17-39.
Oliveira, M.J., da Silva, J.L., Streit, L.: Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals. Acta Applicandae Mathematicae. 113, 17-39 (2011).
Oliveira, Maria Joao, da Silva, Jose Luis, and Streit, Ludwig. “Intersection Local Times of Independent Fractional Brownian Motions as Generalized White Noise Functionals”. Acta Applicandae Mathematicae 113.1 (2011): 17-39.
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