相关论文: Convex Entropy Decay via the Bochner-Bakry-Emery a…
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the notion of measure-valued entropy solutions. Further we survey…
We investigate free-energy dissipation in a continuous-time birth-and-death dynamics in $\mathbb{R}^d$. For these Markov processes, the class of reversible measures coincides with the infinite-volume Gibbs point processes for some…
We consider Fokker-Planck equations in the whole Euclidean space, driven by Levy processes, under the action of confining drifts, as in the classical Ornstein-Ulhenbeck model. We introduce a new PDE method to get exponential or…
In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure…
We prove the exponential convergence to the equilibrium, quantified by R\'enyi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictly convex potential. This extends the classical exponential…
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 variable. For this class of equations, we first establish that…
We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Shannon entropy convergence rates. In the case when they…
Relative entropy, as a divergence metric between two distributions, can be used for offline change-point detection and extends classical methods that mainly rely on moment-based discrepancies. To build a statistical test suitable for this…
The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalised…
Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…
We consider solutions to the Kac master equation for initial conditions where $N$ particles are in a thermal equilibrium and $M\le N$ particles are out of equilibrium. We show that such solutions have exponential decay in entropy relative…
Equilibrium measures are special invariant measures of chaotic dynamical systems and iterated function systems, commonly studied as salient examples of fractal measures. While useful analytic expressions are rare, computational exploration…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
It is well known that open dynamical systems can admit an uncountable number of (absolutely continuous) conditionally invariant measures (ACCIMs) for each prescribed escape rate. We propose and illustrate a convex optimisation based…
This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain $\mathbb{T}^3$, using the…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
We consider a rather general class of non-local in time Fokker-Planck equations and show by means of the entropy method that as $t\to \infty$ the solution converges in $L^1$ to the unique steady state. Important special cases are the…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes.