Phi-entropy inequalities for diffusion semigroups

Abstract

We obtain and study new $\Phi$-entropy inequalities for diffusion semigroups, with Poincaré or logarithmic Sobolev inequalities as particular cases. From this study we derive the asymptotic behaviour of a large class of linear Fokker-Plank type equations under simple conditions, widely extending previous results. Nonlinear diffusion equations are also studied by means of these inequalities. The ${\Gamma }_2$ criterion of D. Bakry and M. Emery appears as a main tool in the analysis, in local or integral forms.

arXiv comment31 pages

References in corpus (1)

• Binomial-Poisson entropic inequalities and the M/M/$\infty$ queue