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arXiv · 1409.1995

Hypercontractivity for Stochastic Hamiltonian Systems

Feng-Yu Wang
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Abstract

The hypercontractivity is proved for the Markov semigroup associated to a class of finite/infinite dimensional stochastic Hamiltonian systems. Consequently, the Markov semigroup is exponentially convergent to the invariant probability measure in entropy (thus, also in $L^2$), and is compact for large time. Since the log-Sobolev inequality is invalid for the associated Dirichlet form, we introduce a general result on the hypercontractivity using the Harnack inequality with power. The main results are illustrated by concrete examples.

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Feng-Yu Wang. 2014-09-06. Hypercontractivity for Stochastic Hamiltonian Systems. https://arxiv.org/abs/1409.1995

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