Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …

We study the relationship between two classical approaches for quantitative ergodic
properties: the first one based on Lyapunov type controls and popularized by Meyn and …

Langevin diffusions are rapidly convergent under appropriate functional inequality
assumptions. Hence, it is natural to expect that with additional smoothness conditions to …

We provide a condition in terms of a supermartingale property for a functional of the Markov
process, which implies (a) f-ergodicity of strong Markov processes at a subgeometric rate …

We revisit functional central limit theorems for additive functionals of ergodic Markov
diffusion processes. Translated in the language of partial differential equations of evolution …

In this paper we intend to give a comprehensive approach of functional inequalities for
diffusion processes under various “curvature” assumptions. One of them coincides with the …

There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via
functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail …

In this paper we derive non asymptotic deviation bounds for {\mathbb P} _\nu (|\frac 1t\int_0^
t V (X_s){\rm d} s-\int V {\rm d}\mu|\geq R) where X is a μ stationary and ergodic Markov …

The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was
shown in [4],[30] that there is an equivalence between a Poincaré inequality, the existence of …

The primary contribution of this thesis is to advance the theory of complexity for sampling
from a continuous probability density over R^ d. Some highlights include: a new analysis of …