Asymptotic analysis of estimators of ergodic stochastic differential equations

TL;DR

This paper investigates the asymptotic behavior of estimators for multidimensional ergodic stochastic differential equations using high-frequency data, establishing their consistency and distributional properties under a general framework.

Contribution

It introduces a more general framework for analyzing estimators of SDEs, including a new approximate maximum likelihood estimator for the drift parameter.

Findings

Proved consistency of the estimators.

Established central limit theorems for the estimators.

Framework applicable to a wider class of models.

Abstract

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of the diffusion parameter and an approximate maximum likelihood estimator of the drift parameter based on a discretized likelihood function have been established in a suitable scaling regime involving the time-gap between the observations and the overall time span. Our framework is more general than that typically considered in the literature and, thus, has the potential to be applicable to a wider range of stochastic models.