We study nonparametric Bayesian modelling of reversible multi-dimensional diffusions with periodic drift. For continuous observations paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The general theorem is applied to standard Gaussian priors , which are shown to converge to the truth at the minimax optimal rate over Sobolev smoothness classes in any dimension . We further establish contraction rates for p-exponential priors over spatially inhomogeneous Besov function classes for which Gaussian priors are unsuitable, again in any dimension.
We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The general theorem is applied to Gaussian priors and p-exponential priors , which are shown to converge to the truth at the minimax optimal rate over Sobolev smoothness classes in any dimension 
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modelling of
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observations
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standard Gaussian priors
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. We further establish contraction rates for p-exponential priors over spatially inhomogeneous Besov function classes for which Gaussian priors are unsuitable, again in any dimension.