This book gives an exposition of the principal concepts and results related to second order
elliptic and parabolic equations for measures, the main examples of which are Fokker …

This survey gives an account of the state of the art of the theory of Ornstein–Uhlenbeck
operators and semigroups. The domains of definition and the spectra of such operators are …

Quantitative long-time entropic convergence and short-time regularization are established
for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian …

We estimate the total variation and Kantorovich distances between transition probabilities of
two diffusions with different diffusion matrices and drifts via a natural quadratic distance …

Principal feature detection via phi-Sobolev inequalities Page 1 Bernoulli 30(4), 2024, 2979–3003
https://doi.org/10.3150/23-BEJ1702 Principal feature detection via φ-Sobolev inequalities …

The classical Bakry-Émery calculus is extended to study, for degenerated (non-elliptic, non-
reversible, or non-diffusive) Markov processes, questions such as hypoellipticity …

We investigate the existence of steady states and exponential decay for hypocoercive
Fokker--Planck equations on the whole space with drift terms that are linear in the position …

We consider three classes of linear non-symmetric Fokker-Planck equations having a
unique steady state and establish exponential convergence of solutions towards the steady …

We study convergence in variation of probability solutions of nonlinear Fokker–Planck–
Kolmogorov equations to stationary solutions. We obtain sufficient conditions for the …

The trend to equilibrium in large time is studied for a large particle system associated to a
Vlasov–Fokker–Planck equation in the presence of a convex external potential, without …