Parameter estimation for fractional mixed fractional Brownian motion based on discrete observations

被引：2

作者：

Ralchenko, Kostiantyn ^{[1
]}

Yakovliev, Mykyta ^{[1
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Kiev, Ukraine

来源：

MODERN STOCHASTICS-THEORY AND APPLICATIONS | 2024年 / 11卷 / 01期

关键词：

Fractional Brownian motion; mixed model; strong consistency; ergodic theorem; asymptotic normality; LIKELIHOOD DRIFT ESTIMATION; GAUSSIAN-PROCESSES; EQUITY WARRANTS; PRICING MODEL;

D O I：

10.15559/23-VMSTA234

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：

The object of investigation is the mixed fractional Brownian motion of the form X-t= kappa B-t(H1) + sigma B-t(H2) , driven by two independent fractional Brownian motions B-1(H) and B-2(H) with Hurst parameters H-1 < H-2. Strongly consistent estimators of unknown model parameters (H-1, H-2, kappa(2), sigma(2))T are constructed based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for 0 < H-1 < H-2 < 3/4.

引用

页码：1 / 29

页数：29

共 33 条

[1]

Arcones M.A., 1994, The Annals of Probability, V22, P2242

[2] MIXED GAUSSIAN PROCESSES: A FILTERING APPROACH [J].