NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES*

doi:10.1007/s10473-024-0107-1

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 143-160.doi: 10.1007/s10473-024-0107-1

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES^*

Yuecai Han^1,2, Dingwen Zhang^1,†

1. School of Mathematics, Jilin University, Changchun 130012, China;
2. Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China

收稿日期:2022-10-25 修回日期:2023-07-23 出版日期:2024-02-25 发布日期:2024-02-27
通讯作者: † Dingwen Zhang, E-mail:zhangdw20@mails.jlu.edu.cn
作者简介:Yuecai Han, E-mail: hanyc@jlu.edu.cn
基金资助:
National Natural Science Foundation of China (11871244), and the Fundamental Research Funds for the Central Universities, JLU.

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES^*

Yuecai Han^1,2, Dingwen Zhang^1,†

1. School of Mathematics, Jilin University, Changchun 130012, China;
2. Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China

Received:2022-10-25 Revised:2023-07-23 Online:2024-02-25 Published:2024-02-27
Contact: † Dingwen Zhang, E-mail:zhangdw20@mails.jlu.edu.cn
About author:Yuecai Han, E-mail: hanyc@jlu.edu.cn
Supported by:
National Natural Science Foundation of China (11871244), and the Fundamental Research Funds for the Central Universities, JLU.

摘要/Abstract

摘要： We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations. The estimates, based on either the continuously observed process or the discretely observed process, are considered. Under certain conditions, we prove the strong consistency and the asymptotic normality of the two estimators. Our method is also suitable for one-sided reflected stochastic differential equations. Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis ${et al.}$ (Stat Sin, 2021, 31: 29-51). Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

关键词: reflected stochastic differential equation, discretely observed process, continuously observed process, Nadaraya-Watson estimator, asymptotic behavior

Abstract: We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations. The estimates, based on either the continuously observed process or the discretely observed process, are considered. Under certain conditions, we prove the strong consistency and the asymptotic normality of the two estimators. Our method is also suitable for one-sided reflected stochastic differential equations. Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis ${et al.}$ (Stat Sin, 2021, 31: 29-51). Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

Key words: reflected stochastic differential equation, discretely observed process, continuously observed process, Nadaraya-Watson estimator, asymptotic behavior

中图分类号:

60F15

Yuecai Han, Dingwen Zhang. NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES^*[J]. 数学物理学报(英文版), 2024, 44(1): 143-160.

Yuecai Han, Dingwen Zhang. NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES^*[J]. Acta mathematica scientia,Series B, 2024, 44(1): 143-160.

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NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES^*

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES^*

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