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Hypercontractivity and applications for stochastic Hamiltonian systems / Feng-yu, Wang

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

Swansea University Author: Feng-yu, Wang

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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
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa32884
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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 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.
Keywords: Hypercontractivity, Stochastic Hamiltonian system, Harnack inequality, Exponential convergence
College: College of Science
Issue: 12
Start Page: 5360
End Page: 5383