Semi Log-Concave Markov Diffusions View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2014

AUTHORS

P. Cattiaux , A. Guillin

ABSTRACT

In this paper we intend to give a comprehensive approach of functional inequalities for diffusion processes under various “curvature” assumptions. One of them coincides with the usual Γ 2 curvature of Bakry and Emery in the case of a (reversible) drifted Brownian motion, but differs for more general diffusion processes. Our approach using simple coupling arguments together with classical stochastic tools, allows us to obtain new results, to recover and to extend already known results, giving in many situations explicit (though non optimal) bounds. In particular, we show new results for gradient/semigroup commutation in the log concave case. Some new convergence to equilibrium in the granular media equation is also exhibited. More... »

PAGES

231-292

Book

TITLE

Séminaire de Probabilités XLVI

ISBN

978-3-319-11969-4
978-3-319-11970-0

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-11970-0_9

DOI

http://dx.doi.org/10.1007/978-3-319-11970-0_9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1019519361


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