STATISTICAL INFERENCE FOR MODELS DRIVEN BY n-TH ORDER FRACTIONAL BROWNIAN MOTION

被引：2

作者：

Chaouch, Hicham ^{[1
]}

El Maroufy, Hamid ^{[1
]}

El Omari, Mohamed ^{[2
]}

机构：

[1] Sultan Mouly Slimane Univ, Fac Sci & Techn, Campus Mghilla,BP 523, BENI MELLAL, Morocco

[2] Chouaib Doukkali Univ, Polydisciplinary Fac Sidi Bennou, BP 299,Jabrane Khalil Jabrane St, El Jadida 24000, Morocco

来源：

THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS | 2023年

关键词：

n-th order fractional Brownian motion; maximum likelihood estimator; least squares estimator; consistency; asymptotic normality; MAXIMUM-LIKELIHOOD ESTIMATOR;

D O I：

10.1090/tpms/1185

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：

. We consider the following stochastic integral equation X(t) = mu t + sigma integral(t)(0) phi(s)dB(H)(n)(s), t >= 0, where phi is a known function and B-H(n) is the n-th order fractional Brownian motion. We provide explicit maximum likelihood estimators for both mu and sigma(2), then we formulate explicitly a least squares estimator for mu and an estimator for sigma(2) by using power variations method. The consistency and asymptotic normality are established for those estimators when the number of observations or the time horizon is sufficiently large.

引用

页码：29 / 43

页数：15

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