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Limit Theorem for Self-intersection Local Time Derivative of Multidimensional Fractional Brownian Motion

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Abstract

The existence condition \(H<1/d\) for first-order derivative of self-intersection local time for \(d\ge 3\) dimensional fractional Brownian motion was obtained in Yu (J Theoret Probab 34(4):1749–1774, 2021). In this paper, we establish a limit theorem under the nonexistence critical condition \(H=1/d\).

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors are grateful to the anonymous referees and editors for their insightful and valuable comments.

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Authors and Affiliations

  1. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Qian Yu

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

    Xianye Yu

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  1. Qian Yu
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  2. Xianye Yu
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Correspondence to Qian Yu.

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Q. Yu is partially supported by the Fundamental Research Funds for the Central Universities (NS2022072), National Natural Science Foundation of China (12201294) and Natural Science Foundation of Jiangsu Province, China (BK20220865). X. Yu is supported by National Natural Science Foundation of China (12071493).

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Yu, Q., Yu, X. Limit Theorem for Self-intersection Local Time Derivative of Multidimensional Fractional Brownian Motion. J Theor Probab (2023). https://doi.org/10.1007/s10959-023-01300-6

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  • DOI: https://doi.org/10.1007/s10959-023-01300-6

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