Nonparametric Bayesian inference for reversible multidimensional diffusions

We study nonparametric Bayesian models for reversible multidimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem the drift gradient vector field under approximation-theoretic conditions on induced prior invariant measure. The applied Gaussian priors and p-exponential priors, which are shown converge truth at optimal over Sobolev smoothness classes in any dimension.