Kernel estimators for q-fractional diffusion processes with random effects using q-calculus

Imen Badrani, Mondher Damak and Yousri Slaoui

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 8, 2429-2450

Abstract: The main purpose of this article is to investigate the kernel estimators for a class of q-analog of fractional stochastic differential equations (q-FSDE) with random effects. Using q-calculus, we first present some properties of the kernel density estimators, such as Bias, variance and we need to introduce the q-analog of Lyapunov’s central limit theorem to prove the q-analog of asymptotic normality of kernel density estimators. Our intention is to use some basic concepts of q-calculus to study the asymptotic behavior of the kernel density estimators for the whole range H∈(12,1). Eventually, we provide an illustrative example, namely q-fractional Langevin equation, to validate the efficacy of our outcomes.

Date: 2025
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DOI: 10.1080/03610926.2024.2369317

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