双分数布朗运动重整化自相交局部时的光滑性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 796-810.

双分数布朗运动重整化自相交局部时的光滑性

桑利恒^1,²,陈振龙^1,*(),郝晓珍¹

¹ 浙江工商大学统计与数学学院杭州 310018
² 滁州学院数学与金融学院安徽滁州 239000

收稿日期:2019-04-01 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 陈振龙 E-mail:zlchen@zjsu.edu.cn
基金资助:
国家自然科学基金(11971432);教育部人文社会科学研究规划基金(18YJA910001);浙江省教育厅科研基金(Y201942401);浙江省一流学科A类（浙江工商大学统计学）

Smoothness for the Renormalized Self-Intersection Local Time of Bifractional Brownian Motion

Liheng Sang^1,²,Zhenlong Chen^1,*(),Xiaozhen Hao¹

¹ School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
² School of Mathematics and Finance, Chuzhou University, Anhui Chuzhou 239000

Received:2019-04-01 Online:2020-06-26 Published:2020-07-15
Contact: Zhenlong Chen E-mail:zlchen@zjsu.edu.cn
Supported by:
the NSFC(11971432);the Humanities and Social Sciences Research Project of Ministry of Education(18YJA910001);the Foundation of Zhejiang Educational Committee(Y201942401);the First Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics)

摘要/Abstract

摘要：

设B^H，K={B^H，K（t），t ≥ 0}是取值于R^d中Hurst指数为H∈（0，1）和K∈（0，1]的双分数布朗运动.它是分数布朗运动的一个推广.该文考虑了B^H，K重整化自相交局部时的光滑性问题.主要运用Malliavin分析中混沌展开的方法，在Meyer-Watanabe意义下，得到了B^H，K重整化自相交局部时是光滑的.该文结论推广了分数布朗运动的相关结果.

关键词: 双分数布朗运动, 重整化自相交局部时, 混沌展开, 光滑性

Abstract:

Let B^{H, K}={B^{H, K}(t), t ≥ 0 } be a bifractional Brownian motion in R^d with Hurst indexes H ∈ (0, 1) and K ∈ (0, 1]. This process constitutes a natural generalization of fractional Brownian motion(which is obtained for K=1). In this paper, we research the smoothness of the renormalized self-intersection local time of B^{H, K}. By the chaos expansion method of Malliavin analysis, we obtain the smoothness of the renormalized self-intersection local time of B^{H, K} in the sense of Meyer-Watanabe. And our result generalizes that of fractional Brownian motion.

Key words: Bifractional Brownian motion, Renormalized self-intersection local time, Chaos expansion, Smoothness

中图分类号:

O211.6

桑利恒,陈振龙,郝晓珍. 双分数布朗运动重整化自相交局部时的光滑性[J]. 数学物理学报, 2020, 40(3): 796-810.

Liheng Sang,Zhenlong Chen,Xiaozhen Hao. Smoothness for the Renormalized Self-Intersection Local Time of Bifractional Brownian Motion[J]. Acta mathematica scientia,Series A, 2020, 40(3): 796-810.

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