Consistent non-parametric Bayesian estimation for a time-inhomogeneous Brownian motion

TL;DR

This paper proves that non-parametric Bayesian methods can reliably estimate the dispersion coefficient of a time-inhomogeneous Brownian motion, ensuring consistent results as data size grows.

Contribution

It establishes posterior consistency for non-parametric Bayesian estimation of the dispersion coefficient in time-inhomogeneous Brownian motion models.

Findings

Posterior distribution concentrates around the true dispersion coefficient.

Consistency holds under mild regularity conditions.

Provides theoretical guarantees for Bayesian non-parametric inference.

Abstract

We establish posterior consistency for non-parametric Bayesian estimation of the dispersion coefficient of a time-inhomogeneous Brownian motion.