Nonparametric Estimation of the Trend Function for Stochastic Processes Driven by Fractional Brownian Motion of the Second Kind  

第二类分数布朗运动驱动的随机过程中趋势函数的非参数估计

作　　者：WANG Yihan ZHANG Xuekang 汪义汉;张雪康(安徽师范大学数学与统计学院,安徽芜湖241002;安徽工程大学数理与金融学院,安徽芜湖241000)

机构地区：[1]School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,China [2]School of Mathematics-Physics and Finance,Anhui Polytechnic University,Wuhu 241000,China

出　　处：《应用数学》2024年第4期885-892,共8页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(12101004);the Natural Science Research Project of Anhui Educational Committee(2023AH030021);the Research Startup Foundation for Introducing Talent of Anhui Polytechnic University(2020YQQ064)。

摘　　要：The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.本文研究第二类分数布朗运动驱动的随机过程中趋势函数的非参数核密度估计问题.首先,探讨了核型估计量的相合性、收敛速率和渐近正态性.其次,证明了核型估计量收敛速率依赖其确定系统的动态行为.

关 键 词：Nonparametric estimation Fractional Brownian motion Uniform consistency Asymptotic normality 

分 类 号：O211.6[理学—概率论与数理统计]