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Local times for multifractional Brownian motion in higher dimensions: A white noise approach

Wolfgang Bock

Technische Universität Kaiserslautern, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern, Germany

E-mail Address: bock@mathematik.uni-kl.de

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José Luís da Silva

CIMA, University of Madeira, Campus da Penteada, 9020-105 Funchal, Portugal

E-mail Address: luis@uma.pt

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Herry P. Suryawan

Department of Mathematics, Sanata Dharma University, Yogyakarta, Indonesia

E-mail Address: herrypribs@usd.ac.id

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https://doi.org/10.1142/S0219025716500260Cited by:1 (Source: Crossref)

Abstract

We present the expansion of the multifractional Brownian motion (mBm) local time in higher dimensions, in terms of Wick powers of white noises (or multiple Wiener integrals). If a suitable number of kernels is subtracted, they exist in the sense of generalized white noise functionals. Moreover, we show the convergence of the regularized truncated local times for mBm in the sense of Hida distributions.

Communicated by U. C. Ji

Keywords:

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