Approximate maximum likelihood estimation for partially observed fractional diffusions from discrete observations
Year: 2026
Type: article
Abstract: This paper studies the problem of parameter estimation for a class of partially observed stochastic di erential equations driven by fractional Brownian motion with Hurst parameter H ∈ (1/2,1). While the continuous-time maximum likelihood estimator (MLE) for such systems has been established in the literature, practical applications typically involve discrete-time observations. We propose an approximate maximum likelihood estimator (AMLE) constructed by discretizing the continuoustime likelihood and replacing the optimal lter with a computationally tractable approximation. Under high-frequency sampling (∆n → 0) and increasing time horizon (T →∞), we establish the strong consistency, law of the iterated logarithm, and asymptotic normality of the proposed estimator. The proofs rely on martingale limit theory and careful control of discretization and lter approximation errors. This work bridges the gap between continuous-time theory and discrete-time implementation for partially observed fractional di usions, providing a solid foundation for statistical inference in this important class of models.
Source: Statistics & Probability Letters
Authors: Thi Hien Nguyen, Kim Duc Tran
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,180
OpenAlex ID: W7214357943