Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion

被引：4

作者：

Lejay A. ^{[1
,2
,3
]}

机构：

[1] Université de Lorraine, IECL, UMR 7502, Vandœuvre-lès-Nancy

[2] CNRS, IECL, UMR 7502, Vandœuvre-lés-Nancy

[3] Inria, Villers-lès-Nancy

来源：

Statistical Inference for Stochastic Processes | 2018年 / 21卷 / 3期

关键词：

Local asymptotic mixed normality; Local time; Maximum likelihood estimator; Null recurrent process; Skew Brownian motion; Skew random walk;

D O I：

10.1007/s11203-017-9161-9

中图分类号：

学科分类号：

摘要：

We study the asymptotic property of simple estimator of the parameter of a skew Brownian motion when one observes its positions on a fixed grid—or equivalently of a simple random walk with a bias at 0. This estimator, nothing more than the maximum likelihood estimator, is based only on the number of passages of the random walk at 0. It is very simple to set up, is consistent and is asymptotically mixed normal. We believe that this simplified framework is helpful to understand the asymptotic behavior of the maximum likelihood of the skew Brownian motion observed at discrete times which is studied in a companion paper. © 2017, Springer Science+Business Media Dordrecht.

引用

页码：539 / 551

页数：12

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