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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 5

Existence and regularization of the local times of a Gaussian process

Herry Pribawanto SURYAWAN
Sayfa
1206–1215
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:We also present a regularization of the local times and show a convergence result in Hida distributions space.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

SURYAWAN, H. P. (2022). Existence and regularization of the local times of a Gaussian process. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 5, 1206–1215. https://ajindex.com/articles/529826

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Kaynakça (11)

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  9. Kondratiev, Y., Leukert, P., Pottho_, J., Streit, L. and Westerkamp, W. Generalized functionals in Gaussian spaces: The characterization theorem revisited, J. Funct. Anal. 141, 301-318, 1996.
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