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Nonparametric estimation for periodic stochastic differential equations driven by fractional G-Brownian motion

Author

Listed:
  • Changhong Guo

    (Guangdong University of Technology, School of Management)

  • Shaomei Fang

    (South China Agricultural University, Department of Mathematics)

  • Yong He

    (Guangdong University of Technology, School of Management)

  • Yong Zhang

    (Guangdong University of Technology, School of Management)

Abstract

This paper investigates the nonparametric estimation problem for some periodic stochastic differential equation driven by fractional G-Brownian motion (fGBm), which generalizes the concepts of the standard Brownian motion, fractional Brownian motion and G-Brownian motion in the framework of sublinear expectation. The fGBm can exhibit long-range dependence and feature the volatility uncertainty simultaneously. Thus it can be a better alternative stochastic process in real applications. First, some probability density function (pdf) called H-G-normal pdf associated with the fGBm is defined, the Volterra representation for fGBm and its Wiener integral are established. Then, the nonparametric estimator for the drift function of the periodic stochastic differential equation is defined by some kernel function, and its consistency and asymptotic distribution are investigated. Finally, some numerical experiments are carried out to illustrate the theoretical results. This study generalizes some well-known existing results of nonparametric estimation.

Suggested Citation

  • Changhong Guo & Shaomei Fang & Yong He & Yong Zhang, 2025. "Nonparametric estimation for periodic stochastic differential equations driven by fractional G-Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 28(3), pages 1-40, December.
    • Handle: RePEc:spr:sistpr:v:28:y:2025:i:3:d:10.1007_s11203-025-09338-5
    DOI: 10.1007/s11203-025-09338-5
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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