Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions
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...
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| Format: | Article |
| Language: | Indonesian |
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Department of Mathematics, FMIPA, Universitas Padjadjaran
2020-02-01
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| Series: | Jurnal Matematika Integratif |
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| Online Access: | http://jurnal.unpad.ac.id/jmi/article/view/23350 |
| Summary: | 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. |
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| ISSN: | 1412-6184 2549-9033 |