Non-parametric Bayesian drift estimation for stochastic differential equations

TL;DR

This paper develops a non-parametric Bayesian method for estimating the drift in stochastic differential equations from discrete data, proving posterior consistency in both one- and multi-dimensional cases under weaker conditions.

Contribution

It introduces a novel Bayesian approach for drift estimation with weaker regularity assumptions and extends posterior consistency results to multidimensional SDEs, a new achievement.

Findings

Posterior consistency established under weaker regularity conditions.

Extension of consistency results to multidimensional SDEs.

Applicable to discrete-time observations of stochastic processes.

Abstract

We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are weaker than those previosly suggested in the literature, we establish posterior consistency in this context. Furthermore, we show that posterior consistency extends to the multidimensional setting as well, which, to the best of our knowledge, is a new result in this setting.