A law of iterated logarithm for the subfractional Brownian motion and an application

被引：0
|
作者：
Qi, Hongsheng [1 ]
Yan, Litan [2 ]
机构：
[1] Bengbu Univ, Coll Sci, Dept Math, Bengbu, Peoples R China
[2] Donghua Univ, Dept Math, Coll Sci, Shanghai, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2018年
基金：
中国国家自然科学基金;
关键词：
Sub-fractional Brownian motion; Iterated logarithm; Phi-variation; PATH PROPERTIES; LIMIT-THEOREMS; TIME;
D O I：
10.1186/s13660-018-1675-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let S-H= {S-t(H), t >= 0} be a sub-fractional Brownian motion with Hurst index 0 < H < 1. In this paper, we give a local law of the iterated logarithm of the form lim sup(s down arrow 0) vertical bar S-t+S(H) - S-t(H)vertical bar/S-H root 2 log(+) log(1/s) = 1, almost surely, for all t > 0, where log(+) x = max{1, log x} for x >= 0. As an application, we introduce the Phi(H)-variation of S-H driven by Phi(H)(x) := [ x/ root 2 log(+) log(+)(1/x)](1/H) (x > 0) with Phi(H)(0) = 0.
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页数：18
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