• Corpus ID: 239024629

# Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups

@inproceedings{Caizo2021HarristypeRO,
title={Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups},
author={Jos{\'e} A. Ca{\~n}izo and St{\'e}phane Mischler},
year={2021}
}
• Published 18 October 2021
• Mathematics
We provide simple and constructive proofs of Harris-type theorems on the existence and uniqueness of an equilibrium and the speed of equilibration of discretetime and continuous-time stochastic semigroups. Our results apply both to cases where the relaxation speed is exponential (also called geometric) and to those with no spectral gap, with non-exponential speeds (also called subgeometric). We give constructive estimates in the subgeometric case and discrete-time statements which seem both to…

## References

SHOWING 1-10 OF 35 REFERENCES
Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations
• Mathematics, Physics
• 2008
We develop a general method to prove the existence of spectral gaps for Markov semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for this analysis is neither a
Ergodic Behavior of Non-conservative Semigroups via Generalized Doeblin’s Conditions
• Mathematics
Acta Applicandae Mathematicae
• 2019
We provide quantitative estimates in total variation distance for positive semigroups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups
Analysis and Geometry of Markov Diffusion Operators
• Mathematics
• 2013
Introduction.- Part I Markov semigroups, basics and examples: 1.Markov semigroups.- 2.Model examples.- 3.General setting.- Part II Three model functional inequalities: 4.Poincare inequalities.-
Hypocoercivity of linear kinetic equations via Harris's Theorem
• Mathematics
• 2019
We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \times \mathbb{R}^d$
Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes
• Mathematics
Transactions of the American Mathematical Society
• 2018
We consider $\mathbb{R}^d$-valued diffusion processes of type \begin{align*} dX_t\ =\ b(X_t)dt\, +\, dB_t. \end{align*} Assuming a geometric drift condition, we establish contractions of the
On Subexponential Convergence to Equilibrium of Markov Processes
Studying the subexponential convergence towards equilibrium of a strong Markov process, we exhibit an intermediate Lyapunov condition equivalent to the control of some moment of a hitting time. This
Fractional Fokker-Planck Equation with General Confinement Force
A Fokker-Planck type equation of fractional diffusion with conservative drift has a property of regularization in fractional Sobolev spaces, as well as a gain of integrability and positivity which it uses to obtain polynomial or exponential convergence to equilibrium in weighted Lebesgue spaces.
Stability of Markovian processes I: criteria for discrete-time Chains
• Mathematics