Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion

被引：28

作者：

Hu, Yaozhong ^{[1
]}

Nualart, David ^{[2
]}

Zhou, Hongjuan ^{[3
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[3] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85281 USA

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2019年 / 91卷 / 08期

基金：

美国国家科学基金会;

关键词：

Fractional Brownian motion; parameter estimation; nonlinear stochastic differential equation; one-sided dissipative Lipschitz condition; maximum inequality; moment estimate; H?lder continuity; strong consistency;

D O I：

10.1080/17442508.2018.1563606

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive the strong consistency of the least squares estimator (LSE) for the drift coefficient of a fractional stochastic differential system. The drift coefficient is one-sided dissipative Lipschitz and the driving noise is additive and fractional with Hurst parameter . We assume that continuous observation is possible. The main tools are ergodic theorem and Malliavin calculus. As a by-product, we derive a maximum inequality for Skorohod integrals, which plays an important role to obtain the strong consistency of the LSE.

引用

页码：1067 / 1091

页数：25

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