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

• Author(s): Oliveira, Maria João ; Silva, José Luís da ; Streit, Ludwig
• Date: 2011
• Persistent ID: http://hdl.handle.net/10400.2/2033
• Origin: Repositório Aberto da Universidade Aberta
• Subject(s): Fractional Brownian motion; White noise analysis; Local time
• Document Type: Journal article
• Language: English
• Contributor(s): Repositório Aberto

Description

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.