Bayesian parameter estimation and prediction in mean reverting stochastic diffusion models

Abstract

We consider the problem of Bayesian parameter estimation and prediction in a diffusion process governed by an Ito stochastic differential equation. The diffusion coefficient function is assumed known while the drift term is an affine function of the state with unknown slope and free coefficients which are assigned a bivariate Gaussian prior distribution. We derive closed-form expressions for the Bayesian predictor of the underlying process and for its mean square accuracy and discuss the conditions under which the posterior parameter uncertainty can be neglected.