Nonlinear Least Squares Estimator for Discretely Observed Reflected Stochastic Processes

TL;DR

This paper develops a nonlinear least squares estimator for reflected stochastic processes observed discretely, establishing its consistency, asymptotic distribution, and demonstrating practical effectiveness through numerical studies.

Contribution

It introduces a novel nonlinear least squares estimation method for discretely observed reflected stochastic processes, with proven theoretical properties and practical validation.

Findings

Estimator is consistent under certain conditions.

Asymptotic distribution of the estimator is derived.

Numerical studies confirm practical applicability.

Abstract

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain conditions, we obtain the consistency and give the asymptotic distribution of the estimator. Moreover, we briefly remark that our method can be extended to the one-sided reflected stochastic processes spontaneously. Numerical studies show that the proposed estimator is adequate for practical use.