Related papers: Binomial-Poisson entropic inequalities and the M/M…
In this paper, we present new Poisson-type deviation inequalities for continuous-time Markov chains whose Wasserstein curvature or $\Gamma$-curvature is bounded below. Although these two curvatures are equivalent for Brownian motion on…
By using the $\Phi$-entropy inequality derived in \cite{Wu, Ch} for Poisson measures, the same type of inequality is established for a class of stochastic differential equations driven by purely jump L\'evy processes. The semigroup…
We study the exponential dissipation of entropic functionals for continuous time Markov chains and the associated convex Sobolev inequalities, including MLSI and Beckner inequalities. We propose a method that combines the Bakry \'Emery…
We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to…
We present some results on Bernstein processes which are Brownian diffusions that appear in Euclidean Quantum Mechanics: We express the distributions of these processes with the help of those of Bessel processes. We then determine two…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…
Our aim is to provide a short and self contained synthesis which generalise and unify various related and unrelated works involving what we call Phi-Sobolev functional inequalities. Such inequalities related to Phi-entropies can be seen in…
Gamma distributions, which contain the exponential as a special case, have a distinguished place in the representation of near-Poisson randomness for statistical processes; typically, they represent distributions of spacings between events…
We study the long time behavior of an Ornstein-Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
We consider $M/Ph/n+M$ queueing systems in steady state. We prove that the Wasserstein distance between the stationary distribution of the normalized system size process and that of a piecewise Ornstein-Uhlenbeck (OU) process is bounded by…
We obtain and study new $\Phi$-entropy inequalities for diffusion semigroups, with Poincar\'e or logarithmic Sobolev inequalities as particular cases. From this study we derive the asymptotic behaviour of a large class of linear…
An upper bound for the Wasserstein distance is provided in the general framework of the Wiener-Poisson space. Is obtained from this bound a second order Poincar\'e-type inequality which is useful in terms of computations. For completeness…
In this paper, the first microscopic approach to the Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended…
We present new $\Phi$-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to…
Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…
We construct a new random probability measure on the sphere and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the…
Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of molecules of mass $m\ll M$ is considered beyond lowest order in the mass ratio $m/M$. The corresponding Langevin equation contains nonlinear corrections to the…