数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 734-754.doi: 10.1007/s10473-020-0311-6

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A LIMIT LAW FOR FUNCTIONALS OF MULTIPLE INDEPENDENT FRACTIONAL BROWNIAN MOTIONS

余迁   

  1. School of Statistics, East China Normal University, Shanghai 200241, China
  • 收稿日期:2018-12-12 修回日期:2019-10-14 出版日期:2020-06-25 发布日期:2020-07-17
  • 作者简介:Qian YU,E-mail:qyumath@163.com
  • 基金资助:
    Q. Yu is partially supported by ECNU Academic Innovation Promotion Program for Excellent Doctoral Students (YBNLTS2019-010) and the Scientific Research Innovation Program for Doctoral Students in Faculty of Economics and Management (2018FEM-BCKYB014).

A LIMIT LAW FOR FUNCTIONALS OF MULTIPLE INDEPENDENT FRACTIONAL BROWNIAN MOTIONS

Qian YU   

  1. School of Statistics, East China Normal University, Shanghai 200241, China
  • Received:2018-12-12 Revised:2019-10-14 Online:2020-06-25 Published:2020-07-17
  • Supported by:
    Q. Yu is partially supported by ECNU Academic Innovation Promotion Program for Excellent Doctoral Students (YBNLTS2019-010) and the Scientific Research Innovation Program for Doctoral Students in Faculty of Economics and Management (2018FEM-BCKYB014).

摘要: Let B={BH(t)}t0 be a d-dimensional fractional Brownian motion with Hurst parameter H(0,1). Consider the functionals of k independent d-dimensional fractional Brownian motions 1nent10entk0f(BH,1(s1)++BH,k(sk))ds1dsk,

where the Hurst index H=k/d. Using the method of moments, we prove the limit law and extending a result by Xu \cite{xu} of the case k=1. It can also be regarded as a fractional generalization of Biane \cite{biane} in the case of Brownian motion.

关键词: Limit theorem, fractional Brownian motion, method of moments, chaining argument

Abstract: Let B={BH(t)}t0 be a d-dimensional fractional Brownian motion with Hurst parameter H(0,1). Consider the functionals of k independent d-dimensional fractional Brownian motions 1nent10entk0f(BH,1(s1)++BH,k(sk))ds1dsk,

where the Hurst index H=k/d. Using the method of moments, we prove the limit law and extending a result by Xu \cite{xu} of the case k=1. It can also be regarded as a fractional generalization of Biane \cite{biane} in the case of Brownian motion.

Key words: Limit theorem, fractional Brownian motion, method of moments, chaining argument

中图分类号: 

  • 60F17