Nonparametric Estimation of Trend Function for Stochastic Differential Equations Driven by a Weighted Fractional Brownian Motion

Authors

Abdelmalik Keddi, Tahar Moulay University of Saida
Fethi Madani, Tahar Moulay University of Saida
Amina A. Bouchentouf, Djillali Liabes University of Sidi Bel Abbes

Abstract

In this paper, we consider the problem of nonparametric estimation of trend function for stochastic differential equations driven by a weighted fractional Brownian motion (weighted-fBm). Under some general conditions, the consistent uniform, the rate of convergence as well as the asymptotic normality of our estimator are established. In addition, a numerical example is provided to illustrate the validity of the considered estimator.

Recommended Citation

Keddi, Abdelmalik; Madani, Fethi; and Bouchentouf, Amina A. (2020). Nonparametric Estimation of Trend Function for Stochastic Differential Equations Driven by a Weighted Fractional Brownian Motion, Applications and Applied Mathematics: An International Journal (AAM), Vol. 15, Iss. 2, Article 2.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/2