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

Oliveira, Maria João; Silva, José Luís da; Streit, Ludwig

http://hdl.handle.net/10400.2/2033

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Authors

Oliveira, Maria João

Silva, José Luís da

Streit, Ludwig

Abstract(s)

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.

Keywords

Fractional Brownian motion White noise analysis Local time

URI

http://hdl.handle.net/10400.2/2033

Citation

Oliveira, Maria João; Silva, José Luís da; Streit, Ludwig - Intersection local times of independent fractional Brownian motions as generalized white noise functionals. "Acta Applicandae Mathematicae" [Em linha]. ISSN 0167-8019. Vol. 113 , nº 1 (2011), p. 17-39