Annals of Probability

Weak Poincaré inequalities for convergence rate of degenerate diffusion processes

Martin Grothaus and Feng-Yu Wang

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aop/1571731441

Digital Object Identifier
doi:10.1214/18-AOP1328

Mathematical Reviews number (MathSciNet)
MR4021241

Zentralblatt MATH identifier
07145307

Subjects
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}

Keywords
Degenerate diffusion semigroup hypocercivity weak Poincaré inequality convergence rate

Citation

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. https://projecteuclid.org/euclid.aop/1571731441


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