• 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}
}
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
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
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
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.-
Subgeometric rates of convergence of f-ergodic strong Markov processes
Hypocoercivity of linear kinetic equations via Harris's Theorem
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
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
TLDR
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
In this paper we connect various topological and probabilistic forms of stability for discrete-time Markov chains. These include tightness on the one hand and Harris recurrence and ergodicity on the
Computable Bounds for Geometric Convergence Rates of Markov Chains
Recent results for geometrically ergodic Markov chains show that there exist constants R < 1; < 1 such that sup jfjjV j Z P n (x; dy)f (y) Z (dy)f (y)j RV (x) n where is the invariant probability
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