## Annals of Probability

### Weak Poincaré inequalities for convergence rate of degenerate diffusion processes

#### 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
Revised: June 2018
First available in Project Euclid: 22 October 2019

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

Digital Object Identifier
doi:10.1214/18-AOP1328

Mathematical Reviews number (MathSciNet)
MR4021241

Zentralblatt MATH identifier
07145307

#### 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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