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Γ-convergence of Onsager–Machlup functionals : II. Infinite product measures on Banach spaces

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Ayanbayev, Birzhan, Klebanov, Ilja, Lie, Han Cheng and Sullivan, T. J. (2021) Γ-convergence of Onsager–Machlup functionals : II. Infinite product measures on Banach spaces. Inverse Problems, 38 (2). 025006. doi:10.1088/1361-6420/ac3f82 ISSN 1361-6420.

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Official URL: https://doi.org/10.1088/1361-6420/ac3f82

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Abstract

We derive Onsager–Machlup functionals for countable product measures on weighted ℓ p subspaces of the sequence space RN . Each measure in the product is a shifted and scaled copy of a reference probability measure on R that admits a sufficiently regular Lebesgue density. We study the equicoercivity and Γ-convergence of sequences of Onsager–Machlup functionals associated to convergent sequences of measures within this class. We use these results to establish analogous results for probability measures on separable Banach or Hilbert spaces, including Gaussian, Cauchy, and Besov measures with summability parameter 1 ⩽ p ⩽ 2. Together with part I of this paper, this provides a basis for analysis of the convergence of maximum a posteriori estimators in Bayesian inverse problems and most likely paths in transition path theory.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
SWORD Depositor: Library Publications Router
Library of Congress Subject Headings (LCSH): Bayesian statistical decision theory, Inverse problems (Differential equations), Functionals, Gaussian measures, Banach spaces, Convergence
Journal or Publication Title: Inverse Problems
Publisher: IOP Publishing
ISSN: 1361-6420
Official Date: 28 December 2021
Dates:
DateEvent
28 December 2021Published
2 December 2021Accepted
Volume: 38
Number: 2
Article Number: 025006
DOI: 10.1088/1361-6420/ac3f82
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 1 February 2022
Date of first compliant Open Access: 1 February 2022
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
415980428[DFG] Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/501100001659
EXC-2046/1 : 390685689[DFG] Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/501100001659
318763901—SFB1294[DFG] Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/501100001659
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