Annals of Probability

Weak Poincaré inequalities for convergence rate of degenerate diffusion processes

Martin Grothaus and Feng-Yu Wang

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For a contraction $C_{0}$-semigroup on a separable Hilbert space, the decay rate is estimated by using the weak Poincaré inequalities for the symmetric and antisymmetric part of the generator. As applications, nonexponential convergence rate is characterized for a class of degenerate diffusion processes, so that the study of hypocoercivity is extended. Concrete examples are presented.

Article information

Ann. Probab., Volume 47, Number 5 (2019), 2930-2952.

Received: March 2017
Revised: June 2018
First available in Project Euclid: 22 October 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 37A25: Ergodicity, mixing, rates of mixing
Secondary: 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}

Degenerate diffusion semigroup hypocercivity weak Poincaré inequality convergence rate


Grothaus, Martin; Wang, Feng-Yu. Weak Poincaré inequalities for convergence rate of degenerate diffusion processes. Ann. Probab. 47 (2019), no. 5, 2930--2952. doi:10.1214/18-AOP1328.

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