Gamma-convergence of Onsager-Machlup functionals
- We derive Onsager-Machlup functionals for countable product measures on weighted l(p) subspaces of the sequence space R-N. 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 Gamma-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.
Author details: | Birzhan AyanbayevORCiD, Ilja KlebanovORCiD, Han Cheng LieORCiD, Tim J. SullivanORCiDGND |
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DOI: | https://doi.org/10.1088/1361-6420/ac3f82 |
ISSN: | 0266-5611 |
ISSN: | 1361-6420 |
Title of parent work (English): | Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data |
Subtitle (English): | II. Infinite product measures on Banach spaces |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/12/28 |
Publication year: | 2021 |
Release date: | 2024/02/01 |
Tag: | Bayesian inverse problems; Gamma-convergence; Onsager-Machlup functional; estimation; maximum a posteriori; small ball probabilities; transition path theory |
Volume: | 38 |
Issue: | 2 |
Article number: | 025006 |
Number of pages: | 35 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG) [415980428]; DFG [TrU-2, EF1-10,; EXC-2046/1, 390685689, 318763901-SFB1294] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |