A parameter estimator based on Smoluchowski-Kramers approximation

TL;DR

This paper introduces a new parameter estimation method for second order stochastic differential equations using the Smoluchowski-Kramers approximation, validated through theoretical consistency and experimental application.

Contribution

It presents a simplified estimator based on a first order system and proves its consistency using { extGamma}-convergence theory, with practical demonstration on colloidal particle movement.

Findings

Estimator is consistent as proven by { extGamma}-convergence.

Method effectively estimates parameters in a colloidal particle movement model.

Experimental results confirm the estimator's practical applicability.

Abstract

We devise a simplified parameter estimator for a second order stochastic differential equation by a first order system based on the Smoluchowski-Kramers approximation. We establish the consistency of the estimator by using {\Gamma}-convergence theory. We further illus- trate our estimation method by an experimentally studied movement model of a colloidal particle immersed in water under conservative force and constant diffusion.