Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions

Herry Pribawanto Suryawan

Abstract


The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others. The increments of sub-fractional Brownian motion is neither independent nor stationary. In this paper we study the sub-fractional Brownian motion using a white noise analysis approach. We recall the represention of sub-fractional Brownian motion on the white noise probability space and show that Donsker's delta functional of a sub-fractional Brownian motion is a Hida distribution. As a main result, we prove the existence of the weighted local times of a $d$-dimensional sub-fractional Brownian motion as Hida distributions.

Keywords


sub-fractional Brownian motion; local times; white noise analysis

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References


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DOI: https://doi.org/10.24198/jmi.v15.n2.23350.81

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Department of Matematics, FMIPA, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang KM. 21 Jatinangor


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