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Hypercontractivity and applications for stochastic Hamiltonian systems

Feng-yu Wang Orcid Logo

Journal of Functional Analysis, Volume: 272, Issue: 12, Pages: 5360 - 5383

Swansea University Author: Feng-yu Wang Orcid Logo

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DOI (Published version): 10.1016/j.jfa.2017.03.015

Abstract

The hypercontractivity is proved for the Markov semigroupassociated with a class of stochastic Hamiltonian systemson Hilbert spaces. Consequently, the Markov semigroup convergesexponentially to the invariant probability measure inentropy and is compact for large time. These strengthen thehypocoerciv...

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Published in: Journal of Functional Analysis
ISSN: 0022-1236
Published: Elsevier BV 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa32884
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first_indexed 2017-04-01T03:49:04Z
last_indexed 2020-08-06T02:52:54Z
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spelling 2020-08-05T11:02:25.6450044 v2 32884 2017-04-01 Hypercontractivity and applications for stochastic Hamiltonian systems 6734caa6d9a388bd3bd8eb0a1131d0de 0000-0003-0950-1672 Feng-yu Wang Feng-yu Wang true false 2017-04-01 SMA The hypercontractivity is proved for the Markov semigroupassociated with a class of stochastic Hamiltonian systemson Hilbert spaces. Consequently, the Markov semigroup convergesexponentially to the invariant probability measure inentropy and is compact for large time. These strengthen thehypocoercivity results derived in the literature. Since the log-Sobolev inequality is invalid, we introduce a new argument toprove the hypercontractivity using coupling and dimensionfreeHarnack inequality. The main results are illustrated byconcrete examples of the kinetic Fokker–Planck equation andhighly degenerate diffusion processes. Journal Article Journal of Functional Analysis 272 12 5360 5383 Elsevier BV 0022-1236 Hypercontractivity, Stochastic Hamiltonian system, Harnack inequality, Exponential convergence 15 6 2017 2017-06-15 10.1016/j.jfa.2017.03.015 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2020-08-05T11:02:25.6450044 2017-04-01T03:16:56.9929332 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Feng-yu Wang 0000-0003-0950-1672 1 0032884-09052017150408.pdf WangHypercontractivity2017.pdf 2017-05-09T15:04:08.5370000 Output 316537 application/pdf Accepted Manuscript true 2018-04-10T00:00:00.0000000 Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true eng
title Hypercontractivity and applications for stochastic Hamiltonian systems
spellingShingle Hypercontractivity and applications for stochastic Hamiltonian systems
Feng-yu Wang
title_short Hypercontractivity and applications for stochastic Hamiltonian systems
title_full Hypercontractivity and applications for stochastic Hamiltonian systems
title_fullStr Hypercontractivity and applications for stochastic Hamiltonian systems
title_full_unstemmed Hypercontractivity and applications for stochastic Hamiltonian systems
title_sort Hypercontractivity and applications for stochastic Hamiltonian systems
author_id_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de
author_id_fullname_str_mv 6734caa6d9a388bd3bd8eb0a1131d0de_***_Feng-yu Wang
author Feng-yu Wang
author2 Feng-yu Wang
format Journal article
container_title Journal of Functional Analysis
container_volume 272
container_issue 12
container_start_page 5360
publishDate 2017
institution Swansea University
issn 0022-1236
doi_str_mv 10.1016/j.jfa.2017.03.015
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description The hypercontractivity is proved for the Markov semigroupassociated with a class of stochastic Hamiltonian systemson Hilbert spaces. Consequently, the Markov semigroup convergesexponentially to the invariant probability measure inentropy and is compact for large time. These strengthen thehypocoercivity results derived in the literature. Since the log-Sobolev inequality is invalid, we introduce a new argument toprove the hypercontractivity using coupling and dimensionfreeHarnack inequality. The main results are illustrated byconcrete examples of the kinetic Fokker–Planck equation andhighly degenerate diffusion processes.
published_date 2017-06-15T03:40:27Z
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score 11.013619

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