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Consistent nonparametric Bayesian inference for discretely observed scalar diffusions. (English) Zbl 1259.62070

Summary: We study Bayes procedures for the problem of nonparametric drift estimation for one-dimensional, ergodic diffusion models from discrete-time, low-frequency data. We give conditions for posterior consistency and verify these conditions for concrete priors, including priors based on wavelet expansions.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62G05 Nonparametric estimation
62F15 Bayesian inference
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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