Consistency of MLE in partially observed diffusion models on a torus

TL;DR

This paper proves that the maximum likelihood estimator for a class of partially observed diffusion models on a torus is consistent, meaning it converges to the true parameter as more data is observed.

Contribution

It establishes the consistency of MLE for partially observed diffusion models with periodic coefficients under regularity conditions.

Findings

MLE converges to the true parameter with increasing sample size

Results apply to models with periodic coefficients on a torus

Provides theoretical foundation for statistical inference in such diffusion models

Abstract

In this paper, we consider a general partially observed diffusion model with periodic coefficients and with non-degenerate diffusion component. The coefficients of such a model depend on an unknown (static and deterministic) parameter which needs to be estimated based on the observed component of the diffusion process. We show that, given enough regularity of the diffusion coefficients, a maximum likelihood estimator of the unknown parameter converges to the true parameter value as the sample size grows to infinity.