Drift parameter estimation for nonlinear reflected stochastic differential equations

TL;DR

This paper investigates the estimation of drift parameters in nonlinear reflected stochastic differential equations using maximum likelihood and least squares methods, establishing their consistency and asymptotic behavior.

Contribution

It introduces and analyzes the asymptotic properties of new estimators for drift parameters in nonlinear reflected SDEs, including cases with one-sided barriers.

Findings

Establishes consistency of the estimators.

Derives asymptotic distributions of the estimators.

Numerical studies confirm practical adequacy.

Abstract

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and give the asymptotic distributions of the two estimators. We briefly remark that our methods could be applied the the reflected stochastic processes with only one-sided reflecting barrier spontaneously. Numerical studies show that the proposed estimators are adequate for practical use.