A LIMIT LAW FOR FUNCTIONALS OF MULTIPLE INDEPENDENT FRACTIONAL BROWNIAN MOTIONS  

作　　者：Qian YU 余迁(School of Statistics,East China Normal University,Shanghai 200241,China)

机构地区：[1]School of Statistics,East China Normal University,Shanghai 200241,China

出　　处：《Acta Mathematica Scientia》2020年第3期734-754,共21页数学物理学报（B辑英文版）

基　　金：Q.Yu is partially supported by ECNU Academic Innovation Promotion Program for Excellent Doctoral Students(YBNLTS2019-010);the Scientific Research Innovation Program for Doctoral Students in Faculty of Economics and Management(2018FEM-BCKYB014).

摘　　要：Let B={B^H(t)}t≥0 be a d-dimensional fractional Brownian motion with Hurst parameter H∈(0,1).Consider the functionals of k independent d-dimensional fractional Brownian motions 1/√n∫0^ent1⋯∫0^entk f(B^H,1(s1)+⋯+B^H,k(sk))ds1⋯dsk,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 

分 类 号：O211.6[理学—概率论与数理统计]