Trajectory fitting estimation for nonlinear stochastic differential equations with reflection

被引：1

作者：

Zhang, Xuekang ^{[1
,2
]}

Shen, Guangjun ^{[3
]}

机构：

[1] Anhui Polytech Univ, Sch Math Phys & Finance, Wuhu 241000, Peoples R China

[2] Anhui Polytech Univ, Key Lab Adv Percept & Intelligent Control Highend, Minist Educ, Wuhu 241000, Peoples R China

[3] Anhui Normal Univ, Dept Stat, Wuhu 241002, Peoples R China

来源：

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS | 2024年 / 38卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Nonlinear stochastic differential equations; reflection; trajectory fitting estimation; consistency; asymptotic distributions; ORNSTEIN-UHLENBECK PROCESS; PARAMETER-ESTIMATION; ASYMPTOTIC-BEHAVIOR; DENSITIES;

D O I：

10.1214/24-BJPS599

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 present paper deals with the problem of trajectory fitting estimation for nonlinear stochastic differential equations with reflection based on continuous -time observation. Under some regularity conditions, the consistency, the rate of convergence and the asymptotic distributions of the trajectory fitting estimator are discussed by using Skorohod equation, Toeplitz lemma and the strong law of large numbers.

引用

页码：177 / 191

页数：15

共 25 条

[1] Parametric estimation for non recurrent diffusion processes [J].

Abi-ayad, Ilham ;

Mourid, Tahar .

STATISTICS & PROBABILITY LETTERS, 2018, 141 :96-102

[2]

Bishwal J.P.N., 2008, LECT NOTES MATH, V1923

[3] Some integral functionals of reflected SDEs and their applications in finance [J].

Bo, Lijun ;

Wang, Yongjin ;

Yang, Xuewei .

QUANTITATIVE FINANCE, 2011, 11 (03) :343-348

[4] Maximum likelihood estimation for reflected Ornstein-Uhlenbeck processes [J].

Bo, Lijun ;

Wang, Yongjin ;

Yang, Xuewei ;

Zhang, Guannan .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2011, 141 (01) :588-596

[5]

Dietz H., 2001, STAT INFER STOCH PRO, V4, P249

[6]

Dietz H. M., 1997, STAT DECIS, V15, P211

[7]

DIETZ HM, 2003, STAT DECIS, V21, P29

[8] MAXIMUM LIKELIHOOD ESTIMATION FOR CONTINUOUS-TIME STOCHASTIC-PROCESSES [J].

FEIGIN, PD .

ADVANCES IN APPLIED PROBABILITY, 1976, 8 (04) :712-736

[9]

Harrison M, 1986, Brownian Motion and Stochastic Flow Systems

[10] Parameter estimation for reflected Ornstein–Uhlenbeck processes with discrete observations [J].

Hu Y. ;

Lee C. ;

Lee M.H. ;

Song J. .

Statistical Inference for Stochastic Processes, 2015, 18 (3) :279-291

← 1 2 3 →