Existence and stability for Fokker–Planck equations with log-concave reference measure View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-11

AUTHORS

Luigi Ambrosio, Giuseppe Savaré, Lorenzo Zambotti

ABSTRACT

We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition probabilities. The main result is the following stability property: if the associated invariant measures converge weakly, then the Markov processes converge in law. The proofs are based on the interpretation of a Fokker–Planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures, endowed with the Wasserstein distance. More... »

PAGES

517-564

References to SciGraph publications

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  • 2002-10. Singular dissipative stochastic equations in Hilbert spaces in PROBABILITY THEORY AND RELATED FIELDS
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  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00440-008-0177-3

    DOI

    http://dx.doi.org/10.1007/s00440-008-0177-3

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