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Local times of linear multifractional stable sheets

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Abstract

Let \(X^{H(u)}(u)=\left\{X^{H(u)}(u), u \in \mathbb{R}_{+}^{N}\right\}\) be linear multifractional stable sheets with index functional H(u), where H(u) = (H1(u),⋯, HN(u)) is a function with values in (0, 1)N. Based on some assumptions of H(u), we obtain the existence of the local times of XH(u)(u) and establish its joint continuity and the Hölder regularity. These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.

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Acknowledgement

The authors are very grateful to the anonymous referees and the editor for their insightful and valuable comments, which have improved the presentation of the paper.

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Authors and Affiliations

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

    Guang-jun Shen

  2. Department of Mathematics, Anhui Normal University, Wuhu, 241000, China

    Guang-jun Shen & Yun-meng Li

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

    Qian Yu

Authors
  1. Guang-jun Shen
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  2. Qian Yu
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  3. Yun-meng Li
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Correspondence to Qian Yu.

Additional information

Supported by the Top Talent Project of University Discipline (speciality) (gxbjZD03), the Distinguished Young Scholars Foundation of Anhui Province (1608085J06), ECNU Academic Innovation Promotion Program for Excellent Doctoral Students (YBNLTS2019-010) and the Scientific Research Innovation Program for Doctoral Students in FFM (2018FEM-BCKYB014).

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Shen, Gj., Yu, Q. & Li, Ym. Local times of linear multifractional stable sheets. Appl. Math. J. Chin. Univ. 35, 1–15 (2020). https://doi.org/10.1007/s11766-020-3548-x

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  • DOI: https://doi.org/10.1007/s11766-020-3548-x

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