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Jaya P. N. Bishwal, Bernstein-von Mises theorem for fractional SPDES with small volatility, Eur. J. Math. Appl. 3 (2023), Article ID 2.

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Volume 3 (2023), Article ID 2

https://doi.org/10.28919/ejma.2023.3.2

Published: 27/01/2023

Abstract:

The Bernstein-von Mises theorem, concerning the convergence of suitably normalized and centred posterior density to normal density, is proved for a certain class of linearly parametrized fractional stochastic partial differential equations (SPDEs) driven by space-time color noise as the volatility decreases to zero. As a consequence, the Bayes estimators of the drift parameter, for smooth loss functions and priors, are shown to be strongly consistent and asymptotically normal, asymptotically efficient and asymptotically equivalent to the maximum likelihood estimator as the volatility decreases to zero. Also computable quasi-posterior density and quasi-Bayes estimators based on finite dimensional projections are shown to have similar asymptotics as the volatility decreases to zero and the dimension of the projection remains fixed.

How to Cite:

Jaya P. N. Bishwal, Bernstein-von Mises theorem for fractional SPDES with small volatility, Eur. J. Math. Appl. 3 (2023), Article ID 2. https://doi.org/10.28919/ejma.2023.3.2