Uniform concentration inequality for ergodic diffusion processes observed at discrete times

被引：9

作者：

Galtchouk, L. ^{[1
]}

Pergamenshchikov, S. ^{[2
]}

机构：

[1] Strasbourg Univ, Dept Math, F-67084 Strasbourg, France

[2] Univ Rouen, Lab Math Raphael Salem, F-76801 St Etienne, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2013年 / 123卷 / 01期

关键词：

Concentration inequality; Ergodic diffusion processes; Geometric ergodicity; Markov chains; Tail distribution; Upper exponential bound;

D O I：

10.1016/j.spa.2012.09.004

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：

In this paper a concentration inequality is proved for the deviation in the ergodic theorem for diffusion processes in the case of discrete time observations. The proof is based on geometric ergodicity of diffusion processes. We consider as an application the nonparametric pointwise estimation problem of the drift coefficient when the process is observed at discrete times. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：91 / 109

页数：19

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