次分数布朗运动的几点注记

J4 ›› 2011, Vol. 46 ›› Issue (3): 102-108.

次分数布朗运动的几点注记

申广君^1,2, 何坤³,闫理坦^3*

1.华东理工大学数学系, 上海 200237; 2.安徽师范大学数学系, 安徽芜湖 241000;
3.东华大学数学系, 上海 201620

收稿日期:2010-05-06 发布日期:2011-04-21
通讯作者: 闫理坦(1961- ), 男,教授,博士生导师,研究方向为随机分析及其应用. Email:litanyan@dhu.edu.cn
作者简介:申广君(1976- ), 男,副教授,博士研究生,研究方向为随机分析及其应用. Email:guangjunshen@yahoo.com.cn
基金资助:
国家自然科学基金资助项目(10871041); 安徽省高等学校省级自然科学研究重点项目(KJ2011A139)

Remarks on sub-fractional Brownian motion

SHEN Guang-jun ^1,2, HE Kun³, YAN Li-tan ^3*

1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;
2. Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui, China;
3. Department of Mathematics, Donghua University, Shanghai 201620, China

Received:2010-05-06 Published:2011-04-21

摘要/Abstract

摘要：

假设 S^H=｛S^H_t,t≥0｝是指标为H∈(0,1) 的次分数Brown运动,证明了当h→+∞时,增量过程 (S^H_h+t-S^H_h,t≥0)依分布收敛于指数H的分数Brown运动,同时讨论了与次分数Brown噪声相关联的极限定理。

关键词: Brown运动; 分数Brown运动; 次分数Brown运动; 拟Dirichlet 过程

Abstract:

Let S^H=｛S^H_t,t≥0｝ be a sub-fractional Brownian motion with index H∈(0,1). It is shown that the increment process generated by the sub-fractional Brownian motion (S^H_h+t-S^H_h,t≥0) converges to a fractional Brownian motion with Hurst index H in the sense of finite dimensional distributions, as h tends to infinity. Also, the limit theorems associated with the subfractional Brownian noise are also studied.

Key words: Brownian motion; fractional Brownian motion; sub-fractional Brownian motion; quasi-Dirichlet process

申广君1,2, 何坤3,闫理坦3*. 次分数布朗运动的几点注记[J]. J4, 2011, 46(3): 102-108.

SHEN Guang-jun 1,2, HE Kun 3, YAN Li-tan 3. Remarks on sub-fractional Brownian motion[J]. J4, 2011, 46(3): 102-108.

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