Non-parametric Bayesian drift estimation for stochastic differential equations

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.

27 pages

References in corpus (5)

• Convergence rates of posterior distributions for noniid observations
• Penalized nonparametric mean square estimation of the coefficients of diffusion processes
• Reversible jump MCMC for nonparametric drift estimation for diffusion processes
• Consistent nonparametric Bayesian inference for discretely observed scalar diffusions
• Non-parametric Bayesian drift estimation for stochastic differential equations

Cited by in corpus (8)

• Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions
• Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions
• Nonparametric Bayesian inference for reversible multi-dimensional diffusions
• Non-parametric Bayesian drift estimation for stochastic differential equations
• Consistency of Bayesian nonparametric inference for discretely observed jump diffusions
• Nonparametric Bayesian estimation of a Hölder continuous diffusion coefficient
• Nonparametric Bayesian volatility estimation
• Nonparametric Bayesian estimation in a multidimensional diffusion model with high frequency data