Prediction of fractional Brownian motion-type processes

被引：5

作者：

Inoue, A.

Anh, V. V.

机构：

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[2] Hokkaido Univ, Fac Sci, Dept Math, Sapporo, Hokkaido 060, Japan

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2007年 / 25卷 / 03期

关键词：

fractional Brownian motion; Hurst index; prediction;

D O I：

10.1080/07362990701282971

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a class of continuous- time Gaussian processes with stationary increments via moving-average representation with good MA coefficient. The class includes fractional Brownian motion with Hurst index less than 1/2 as a typical example. It also includes processes which have different indices corresponding to the local and long-time properties, repsectively. We derive some basic properties of the processes, and, using the results, we establish a prediction formula for them. The prediction kernel in the formula is given explicitly in terms of MA and AR coefficients.

引用

页码：641 / 666

页数：26

共 15 条

[1]

Adler R. J., 1981, GEOMETRY RANDOM FIEL

[2] Financial markets with memory II: Innovation processes and expected utility maximization [J].