Nonparametric estimation for stochastic differential equations driven by mixed fractional Brownian motion with random effects
The paper under review deals with the problem of nonparametric estimation of the density of random effects in models governed by a stochastic differential equation driven by a mixed fractional Brownian motion. The author starts with an overview of some properties of stochastic processes, which are solutions of stochastic differential equations driven by a mixed fractional Brownian motion. Next, he proceeds with introducing a computable estimator of the unknown random effects' density function and proves its consistency in a way analogous to [\textit{M. El Omari} et al., Statistics 53, No. 4, 753--769 (2019; Zbl 1440.62318)], thus indicating that similar results continue to hold for processes driven by a mixed fractional Brownian motion. Finally, the asymptotic distribution of the proposed estimator is derived.
scientific article; zbMATH DE number 7389299
scientific article