4.3 Article

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

期刊

出版社

ELSEVIER
DOI: 10.1016/j.spa.2023.104239

关键词

Drift and diffusion estimation; Ito diffusion process; Local linear smoothing; Nonparametric estimation; SDE; FDA; Brownian motion

向作者/读者索取更多资源

This study considers the nonparametric estimation of the drift and diffusion coefficients in a Stochastic Differential Equation (SDE) using functional data analysis methods. The proposed estimators relate local parameters to global parameters through a novel Partial Differential Equation (PDE) and do not require any specific functional form assumptions. The study establishes almost sure uniform asymptotic convergence rates for the estimators, taking into account the impact of different sampling frequencies.
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} and f3 is an element of {0 , 1/2 , 1} , which includes prominent examples such as Brownian motion, Ornstein-Uhlenbeck process, geometric Brownian motion and Brownian bridge. Our estimators are constructed by relating the local (drift/diffusion) parameters of the SDE to its global parameters (mean/covariance, and their derivatives) by means of an apparently novel Partial Differential Equation (PDE). This allows us to use methods inspired by functional data analysis, and pool information across the sparsely measured paths. The methodology we develop is fully non-parametric and avoids any functional form specification on the time-dependency of either the drift function or the diffusion function. We establish almost sure uniform asymptotic convergence rates of the proposed estimators as the number of observed paths n grows to infinity. Our rates are non-asymptotic in the number of measurements per path, explicitly reflecting how different sampling frequency might affect the speed of convergence. Our framework suggests possible further fruitful interactions between FDA and SDE methods in problems with replication.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.3
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据