The Lévy–Fokker–Planck equation: Φ-entropies and convergence to equilibrium
نویسندگان
چکیده
منابع مشابه
The Lévy-Fokker-Planck equation: Φ-entropies and convergence to equilibrium
In this paper, we study a Fokker-Planck equation of the form ut = I[u] + div(xu) where the operator I, which is usually the Laplacian, is replaced here with a general Lévy operator. We prove by the entropy production method the exponential decay in time of the solution to the only steady state of the associated stationnary equation.
متن کاملThe Lévy-Fokker-Planck equation: Phi-entropies and convergence to equilibrium
In this paper, we study a Fokker-Planck equation of the form ut = I[u] + div(xu) where the operator I, which is usually the Laplacian, is replaced here with a general Lévy operator. We prove by the entropy production method the exponential decay in time of the solution to the only steady state of the associated stationnary equation.
متن کاملConvergence to Equilibrium for the Linearized Cometary Flow Equation
We study convergence to equilibrium for certain spatially inhomogenous kinetic equations, such as discrete velocity models or a linearization of a kinetic model for cometary flow. For such equations, the convergence to a unique equilibrium state is the result of, firstly, the dissipative effects of the collision operator, which morphs the solution towards an entropy minimizing local equilibrium...
متن کاملdeBruijn identities: from Shannon, Kullback–Leibler and Fisher to generalized φ -entropies, φ -divergences and φ -Fisher informations
In this paper we propose a generalization of the usual deBruijn identity that links the Shannon differential entropy (or the Kullback–Leibler divergence) and the Fisher information (or the Fisher divergence) of the output of a Gaussian channel. The generalization makes use of φ -entropies on the one hand, and of φ -divergences (of the Csizàr class) on the other hand, as generalizations of the S...
متن کاملMod-φ Convergence
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex brownian motion and the classical situation of the central limit theorem, and a conjecture concerning the distribution of values of the Riemann zeta function on the critical line.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Asymptotic Analysis
سال: 2008
ISSN: 0921-7134
DOI: 10.3233/asy-2008-0887