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Derivatives of Intersection Local Time for Two Independent Symmetric α-stable Processes

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Abstract

In this paper, we consider the derivatives of intersection local time for two independent d-dimensional symmetric α-stable processes Xα and \({\widetilde X^{\widetilde \alpha }}\) with respective indices α and \(\widetilde \alpha \). We first study the sufficient condition for the existence of the derivatives, which makes us obtain the exponential integrability and Hölder continuity. Then we show that this condition is also necessary for the existence of derivatives of intersection local time at the origin. Moreover, we also study the power variation of the derivatives.

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Acknowledgements

We thank the referees and the editor for their time and comments.

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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241002, P. R. China

    Huan Zhou & Guang Jun Shen

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, P. R. China

    Qian Yu

  3. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 211106, P. R. China

    Qian Yu

Authors
  1. Huan Zhou
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  2. Guang Jun Shen
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  3. Qian Yu
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Correspondence to Qian Yu.

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Conflict of Interest The authors declare no conflict of interest.

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Supported by National Natural Science Foundation of China (Grant Nos. 12071003, 12201294) and Natural Science Foundation of Jiangsu Province, China (Grant No. BK20220865)

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Zhou, H., Shen, G.J. & Yu, Q. Derivatives of Intersection Local Time for Two Independent Symmetric α-stable Processes. Acta. Math. Sin.-English Ser. 40, 1273–1292 (2024). https://doi.org/10.1007/s10114-023-2516-9

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  • DOI: https://doi.org/10.1007/s10114-023-2516-9

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