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

被引：0
作者：
Qian Yu
机构：
[1] Nanjing University of Aeronautics and Astronautics,Department of Mathematics
[2] School of Statistics,undefined
[3] East China Normal University,undefined
来源：
Journal of Theoretical Probability | 2021年 / 34卷
关键词：
Self-intersection local time; Fractional Brownian motion; Hölder continuity; 60G22; 60J55;
D O I：
暂无
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学科分类号：
摘要：
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=(k1,k2,…,kd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k=(k_1,k_2,\ldots , k_d)$$\end{document}. Moreover, we show a limit theorem for the critical case with H=23\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H=\frac{2}{3}$$\end{document} and d=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=1$$\end{document}, which was conjectured by Jung and Markowsky [7].
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页码：1749 / 1774
页数：25
相关论文
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