Approximate maximum likelihood estimation for partially observed fractional diffusions from discrete observations
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.
Related
- Broadly Applicable Approximate MCMC for Switching Stochastic Differential Equations Using Uniformization and Time-Conditioned Factorized Neural Likelihood Estimation
- Optimal guaranteed sequential estimation for mean-reverting CEV diffusions
- Geometry and observability of latent texture-coherence diffusions in coherent sea-clutter radar observations
- Sticky-threshold diffusions, local time approximation and parameter estimation
- Elasticity estimation via the CKLS--CIR transform for small-noise CEV-type diffusions
BibTeX
@article{nguyen2026approximate,
title = {{Approximate maximum likelihood estimation for partially observed fractional diffusions from discrete observations}},
author = {Thi Hien Nguyen and Kim Duc Tran},
journal = {Statistics \& Probability Letters},
year = {2026},
month = oct,
doi = {10.1016/j.spl.2026.110982},
url = {https://hal.science/hal-05805762v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Approximate maximum likelihood estimation for partially observed fractional diffusions from discrete observations
AU - Thi Hien Nguyen
AU - Kim Duc Tran
PY - 2026
DA - 2026/10/19
JO - Statistics & Probability Letters
DO - 10.1016/j.spl.2026.110982
UR - https://hal.science/hal-05805762v1
AB - 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.
SN - 0167-7152
SN - 1879-2103
ER -