Asymptotic inference for stochastic differential equations driven by fractional Brownian motion

被引：0
作者：
Shohei Nakajima
Yasutaka Shimizu
机构：
[1] Waseda University,Department of Applied Mathematics
来源：
Japanese Journal of Statistics and Data Science | 2023年 / 6卷
关键词：
Parameter estimation; Stochastic differential equation; Fractional Brownian motion; Multiplicative noise; Small noise asymptotics; 61F12; 60G22; 62M09;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study a problem of parametric estimation for continuously observed stochastic processes involving fractional Brownian motion with Hurst index H∈(1/2,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H\in (1/2,1)$$\end{document}. Under some assumptions on the drift and volatility coefficients, we obtain the asymptotic normality and moment convergence of maximum likelihood type estimator of the drift parameter under the small noise asymptotics such that the driving noise vanishes.
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页码：431 / 455
页数：24
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