Elliptic equations for invariant measures on finite and infinite dimensional manifolds

Bogachev VI, Röckner M, Wang F-Y (2001)
Journal de Mathématiques Pures et Appliquées 80(2): 177-221.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bogachev, Vladimir I.; Röckner, MichaelUniBi; Wang, Feng-Yu
Abstract / Bemerkung
We obtain sufficient conditions in terms of Lyapunov functions for the existence of invariant measures for diffusions on finite-dimensional manifolds and prove some regularity results for such measures. These results are extended to countable products of finite-dimensional manifolds. We introduce and study a new concept of weak elliptic equations for measures on infinite-dimensional manifolds. Then we apply our results to Gibbs distributions in the case where the single spin spaces are Riemannian manifolds. In particular, we obtain some a priori estimates for such Gibbs distributions and prove a general existence result applicable to a wide class of models. We also apply our techniques to prove absolute continuity of invariant measures on the infinite-dimensional torus, improving a recent result of A.F. Ramirez. Furthermore, we obtain a new result concerning the question whether invariant measures are Gibbsian. (C) 2001 Editions scientifiques et medicales Elsevier SAS.
Stichworte
elliptic equations for; measures; Lyapunov functions; Gibbs distributions; logarithmic gradients; invariant measures; diffusions on manifolds
Erscheinungsjahr
2001
Zeitschriftentitel
Journal de Mathématiques Pures et Appliquées
Band
80
Ausgabe
2
Seite(n)
177-221
ISSN
0021-7824
Page URI
https://pub.uni-bielefeld.de/record/1617754

Zitieren

Bogachev VI, Röckner M, Wang F-Y. Elliptic equations for invariant measures on finite and infinite dimensional manifolds. Journal de Mathématiques Pures et Appliquées. 2001;80(2):177-221.
Bogachev, V. I., Röckner, M., & Wang, F. - Y. (2001). Elliptic equations for invariant measures on finite and infinite dimensional manifolds. Journal de Mathématiques Pures et Appliquées, 80(2), 177-221. https://doi.org/10.1016/S0021-7824(00)01187-9
Bogachev, V. I., Röckner, M., and Wang, F. - Y. (2001). Elliptic equations for invariant measures on finite and infinite dimensional manifolds. Journal de Mathématiques Pures et Appliquées 80, 177-221.
Bogachev, V.I., Röckner, M., & Wang, F.-Y., 2001. Elliptic equations for invariant measures on finite and infinite dimensional manifolds. Journal de Mathématiques Pures et Appliquées, 80(2), p 177-221.
V.I. Bogachev, M. Röckner, and F.-Y. Wang, “Elliptic equations for invariant measures on finite and infinite dimensional manifolds”, Journal de Mathématiques Pures et Appliquées, vol. 80, 2001, pp. 177-221.
Bogachev, V.I., Röckner, M., Wang, F.-Y.: Elliptic equations for invariant measures on finite and infinite dimensional manifolds. Journal de Mathématiques Pures et Appliquées. 80, 177-221 (2001).
Bogachev, Vladimir I., Röckner, Michael, and Wang, Feng-Yu. “Elliptic equations for invariant measures on finite and infinite dimensional manifolds”. Journal de Mathématiques Pures et Appliquées 80.2 (2001): 177-221.

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