Elliptic equations for infinite dimensional probability distributions and Lyapunov functions

Authors
Bogachev, V Rockner, M
Citation
V. Bogachev et M. Rockner, Elliptic equations for infinite dimensional probability distributions and Lyapunov functions, CR AC S I, 329(8), 1999, pp. 705-710
Citations number
7
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
329
Issue
8
Year of publication
1999
Pages
705 - 710
Database
ISI
SICI code
0764-4442(19991015)329:8<705:EEFIDP>2.0.ZU;2-Z
Abstract
A new concept of a weak elliptic equation for probability distributions on infinite dimensional spaces is introduced. A suitable notion of a Lyapunov function is defined for weak elliptic equations. Sufficient conditions in t erms of Lyapunov functions are given for the existence of solutions for wea k elliptic equations. Applications to Gibbs measures are discussed. (C) 199 9 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.