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Existence and Smoothness of Local Time and Self-intersection Local Time for Spherical Gaussian Random Fields

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Abstract

In this paper, we study properties of local time for spherical Gaussian random fields T on \({\mathbb{S}^2}\). For 2 < α < 4, we give a formally expression of local time for spherical Gaussian random fields, and obtain that the existence of local time in L2 if and only if (α − 2)d < 4 and the smoothness in the sense of Meyer–Watanabe if and only if (α − 2)(d + 2) < 4, respectively. Finally, the existence and smoothness of self-intersection local time of T are considered.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11971432), the Management Project of “Digital+” Discipline Construction of Zhejiang Gongshang University (Nos. SZJ2022A012, SZJ2022B017), the Natural Science Foundation of Zhejiang Province (No. LY21G010003), the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (No. GXYQ2020058) and Collaborative Innovation Center of Statistical Data Engineering Technology & Application.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China

    Liheng Sang & Zhenlong Chen

  2. School of Mathematics and Finance, Chuzhou University, Chuzhou, 239000, China

    Liheng Sang

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  1. Liheng Sang
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  2. Zhenlong Chen
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Correspondence to Zhenlong Chen.

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Sang, L., Chen, Z. Existence and Smoothness of Local Time and Self-intersection Local Time for Spherical Gaussian Random Fields. Front. Math 18, 591–614 (2023). https://doi.org/10.1007/s11464-021-0087-6

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  • DOI: https://doi.org/10.1007/s11464-021-0087-6

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