次分数布朗运动的Hermite变差(英文)

Hermite Variation of Subfractional Brownian Motion

本文主要研究了H∈(0,1)时次分数布朗运动的q次赋权Hermite变差的一些中心极限定理,其中q为整数且q≥2.当1/(2_q)<H≤1-1/(2_q)时,中心极限定理成立,且其极限为一个条件高斯分布.当H<1/(2_q)时,赋权Hermit.e变差L^2收敛,且其极限仅依赖于次分数布朗运动.

The aim of this paper is to derive some central limit theorems for the weighted Hermite variations of order q 〉 2 of the subfractional Brownian motion with H E （0, 1）, where q is an integer. The central limit theorem holds for 1/2q〈H≤1-1/2q the limit being a conditionally Gaussian distribution. If H 〈 1/qq,we show the convergence in L^2 to a limit which only depends on the subfractional Brownian motion.