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November 2019 Nonparametric Bayesian posterior contraction rates for scalar diffusions with high-frequency data
Kweku Abraham
Bernoulli 25(4A): 2696-2728 (November 2019). DOI: 10.3150/18-BEJ1067

Abstract

We consider inference in the scalar diffusion model $\,\mathrm{d}X_{t}=b(X_{t})\,\mathrm{d}t+\sigma(X_{t})\,\mathrm{d}W_{t}$ with discrete data $(X_{j\Delta_{n}})_{0\leq j\leq n}$, $n\to\infty$, $\Delta_{n}\to0$ and periodic coefficients. For $\sigma$ given, we prove a general theorem detailing conditions under which Bayesian posteriors will contract in $L^{2}$-distance around the true drift function $b_{0}$ at the frequentist minimax rate (up to logarithmic factors) over Besov smoothness classes. We exhibit natural nonparametric priors which satisfy our conditions. Our results show that the Bayesian method adapts both to an unknown sampling regime and to unknown smoothness.

Citation

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Kweku Abraham. "Nonparametric Bayesian posterior contraction rates for scalar diffusions with high-frequency data." Bernoulli 25 (4A) 2696 - 2728, November 2019. https://doi.org/10.3150/18-BEJ1067

Information

Received: 1 February 2018; Revised: 1 July 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110109
MathSciNet: MR4003562
Digital Object Identifier: 10.3150/18-BEJ1067

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 4A • November 2019
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