NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES  

作　　者：韩月才 张丁文 Yuecai HAN;Dingwen ZHANG(School of Mathematics,Jilin University,Changchun,130012,China;Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University,Changchun,130012,China)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2024年第1期143-160,共18页数学物理学报（B辑英文版）

基　　金：partially supported by the National Natural Science Foundation of China(11871244);the Fundamental Research Funds for the Central Universities,JLU。

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 

分 类 号：O211.6[理学—概率论与数理统计]