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• W1768770245 abstract "We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_Delta, dots, X_{nDelta}$. We analyse the nonlinear inverse problem corresponding to the `low frequency sampling' regime where $Delta>0$ is fixed and $n to infty$. A general theorem is proved that gives conditions for prior distributions $Pi$ on the diffusion coefficient $sigma$ and the drift function $b$ that ensure minimax optimal contraction rates of the posterior distribution over Holder-Sobolev smoothness classes. These conditions are verified for natural examples of nonparametric random wavelet series priors. For the proofs we derive new concentration inequalities for empirical processes arising from discretely observed diffusions that are of independent interest." @default.
• W1768770245 created "2016-06-24" @default.
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• W1768770245 date "2017-08-01" @default.
• W1768770245 modified "2023-10-14" @default.
• W1768770245 title "Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions" @default.
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• W1768770245 doi "https://doi.org/10.1214/16-aos1504" @default.
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