Remarks on an integral functional driven by sub-fractional Brownian motion

被引:17
作者
Shen, Guangjun [2 ,3 ]
Yan, Litan [1 ]
机构
[1] Donghua Univ, Dept Math, Shanghai 201620, Peoples R China
[2] E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China
[3] Anhui Normal Univ, Dept Math, Wuhu 241000, Peoples R China
关键词
Sub-fractional Brownian motion; Local time; Self-intersection local time; p-variation; Stochastic area integrals; LOCAL TIME; RESPECT;
D O I
10.1016/j.jkss.2010.12.004
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
This paper studies the functionals A(1) (t, x) = integral(t)(0) 1([0,infinity))(x - S-s(H))ds, A(2)(t, x) = integral(t)(0) 1([0,infinity))(x - S-s(H))s(2H-1)ds, where (S-t(H))(0 <= t <= T) is a one-dimension sub-fractional Brownian motion with index H is an element of (0, 1). It shows that there exists a constant P-H is an element of (1, 2) such that p-variation of the process A(j)(t, S-t(H)) - integral(t)(0) L-j(s, S-s(H))dS(s)(H) (j = 1, 2) is equal to 0 if p > p(H), where L-j = 1, 2, are the local time and weighted local time of S-H, respectively. This extends the classical results for Brownian motion. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码:337 / 346
页数:10
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