Experiment design for controlled partially observed fractional diffusion process

TL;DR

This paper develops an asymptotic experiment design and efficient estimation method for a controlled second-order differential equation with partial observation and fractional noise, focusing on large observation times.

Contribution

It introduces a novel asymptotic design framework and a one-step Newton-Raphson estimator for unknown parameters in a fractional diffusion process.

Findings

Efficient estimator for the unknown drift parameter is proposed.

Asymptotic design strategies are developed for large observation times.

The one-step estimation procedure improves estimation accuracy.

Abstract

We consider a controlled second order differential equation which is partially observed with an additional fractional noise. we study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of the unknown signal drift parameter. When the input depends on the unknow parameter, we will try the one-step estimation procedure using the Newton-Raphson method.