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A hypocoercivity related ergodicity method for Kolmogorov equations
Author(s) -
Grothaus Martin,
Stilgenbauer Patrik
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410484
Subject(s) - ergodicity , operator (biology) , degenerate energy levels , mathematics , convergence (economics) , statistical physics , dynamical systems theory , rate of convergence , mathematical physics , pure mathematics , mathematical analysis , physics , computer science , economics , statistics , quantum mechanics , computer network , biochemistry , chemistry , channel (broadcasting) , repressor , transcription factor , gene , economic growth
We develop a new abstract strategy for proving ergodicity with explicit computable rate of convergence for diffusions associated with a degenerate Kolmogorov operator L . A crucial point is that the evolution operator L may have singular and nonsmooth coefficients. This allows the application of the method e.g. to the degenerate N particle Langevin dynamics. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)