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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 47 Issue: 5

Existence and regularization of the local times of a Gaussian process

Herry Pribawanto Suryawan(DEPARTMENT OF MATHEMATICS, SANATA DHARMA UNIVERSITY)
Pages
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Publication Date
2018-10-16
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also present a regularization of the local times and show a convergence result in Hida distributions space.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We study an existence result in the mean square sense of the local times of a one-dimensional Gaussian process defined by an indefinite Wiener integral.
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Key Findings & Data:For any spatial dimension, we prove that the local times of a Gaussian process, after appropriatelly renormalized, exist as White noise distributions.
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Conclusion & Impact:We also present a regularization of the local times and show a convergence result in Hida distributions space.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Local times · b-Gaussian process · white noise analysis.

Abstract

We study an existence result in the mean square sense of the local times of a one-dimensional Gaussian process defined by an indefinite Wiener integral. For any spatial dimension, we prove that the local times of a Gaussian process, after appropriatelly renormalized, exist as White noise distributions. We also present a regularization of the local times and show a convergence result in Hida distributions space.

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Cite This Article

Suryawan, H. P. (2018). Existence and regularization of the local times of a Gaussian process. Hacettepe Journal of Mathematics and Statistics, Volume: 47 Issue: 5. https://ajindex.com/articles/1402889

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