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Higher-Order Derivative of Self-Intersection Local Time for Fractional Brownian Motion

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Abstract

We consider the existence and Hölder continuity conditions for the k-th-order derivatives of self-intersection local time for d-dimensional fractional Brownian motion, where \(k=(k_1,k_2,\ldots , k_d)\). Moreover, we show a limit theorem for the critical case with \(H=\frac{2}{3}\) and \(d=1\), which was conjectured by Jung and Markowsky [7].

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Acknowledgements

I would like to sincerely thank my supervisor Professor Fangjun Xu, who has led the way to this work. I am also grateful to the anonymous referee and Associate Editor for their insightful and valuable comments which have greatly improved the presentation of the paper. Q. Yu is supported by National Natural Science Foundation of China (Grant No.11871219, 12071003).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Qian Yu

  2. School of Statistics, East China Normal University, Shanghai, 200062, China

    Qian Yu

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Correspondence to Qian Yu.

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Yu, Q. Higher-Order Derivative of Self-Intersection Local Time for Fractional Brownian Motion. J Theor Probab 34, 1749–1774 (2021). https://doi.org/10.1007/s10959-021-01093-6

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  • DOI: https://doi.org/10.1007/s10959-021-01093-6

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