Journal article 1119 views 141 downloads
Hypercontractivity and applications for stochastic Hamiltonian systems
Journal of Functional Analysis, Volume: 272, Issue: 12, Pages: 5360 - 5383
Swansea University Author:
Feng-yu Wang
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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...
| Published in: | Journal of Functional Analysis |
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| ISSN: | 0022-1236 |
| Published: |
Elsevier BV
2017
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| Online Access: |
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| 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. |
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| Keywords: |
Hypercontractivity, Stochastic Hamiltonian system, Harnack inequality, Exponential convergence |
| College: |
Faculty of Science and Engineering |
| Issue: |
12 |
| Start Page: |
5360 |
| End Page: |
5383 |