Elliptic equations for measures on infinite dimensional spaces and applications

Bogachev VI, Röckner M (2001)
Probability Theory and Related Fields 120(4): 445-496.

Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Zeitschriftenaufsatz | Veröffentlicht | Englisch
Autor
;
Abstract / Bemerkung
We introduce and study a new concept of a weak elliptic equation for measures on infinite dimensional spaces. This concept allows one to consider equations whose coefficients are not globally integrable. By using a suitably extended Lyapunov function technique, we derive a priori estimates for the solutions of such equations and prove new existence results. As an application, we consider stochastic Burgers, reaction-diffusion, and Navier-Stokes equations and investigate the elliptic equations for the corresponding invariant measures. Our general theorems yield a priori estimates and existence results for such elliptic equations. We also obtain moment estimates for Gibbs distributions and prove an existence result applicable to a wide class of models.
Erscheinungsjahr
Zeitschriftentitel
Probability Theory and Related Fields
Band
120
Ausgabe
4
Seite(n)
445-496
ISSN
PUB-ID

Zitieren

Bogachev VI, Röckner M. Elliptic equations for measures on infinite dimensional spaces and applications. Probability Theory and Related Fields. 2001;120(4):445-496.
Bogachev, V. I., & Röckner, M. (2001). Elliptic equations for measures on infinite dimensional spaces and applications. Probability Theory and Related Fields, 120(4), 445-496. doi:10.1007/PL00008789
Bogachev, V. I., and Röckner, M. (2001). Elliptic equations for measures on infinite dimensional spaces and applications. Probability Theory and Related Fields 120, 445-496.
Bogachev, V.I., & Röckner, M., 2001. Elliptic equations for measures on infinite dimensional spaces and applications. Probability Theory and Related Fields, 120(4), p 445-496.
V.I. Bogachev and M. Röckner, “Elliptic equations for measures on infinite dimensional spaces and applications”, Probability Theory and Related Fields, vol. 120, 2001, pp. 445-496.
Bogachev, V.I., Röckner, M.: Elliptic equations for measures on infinite dimensional spaces and applications. Probability Theory and Related Fields. 120, 445-496 (2001).
Bogachev, Vladimir I., and Röckner, Michael. “Elliptic equations for measures on infinite dimensional spaces and applications”. Probability Theory and Related Fields 120.4 (2001): 445-496.