Onsager Machlup functional for stochastic evolution equations in a class of norms

Xavier Bardina, Carles Rovira and Samy Tindel

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona,Spain
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007-Barcelona, Spain
Département de Mathématiques, Institut Galilée - Université Paris 13, Avenue J. B. Clément, 93430-Villetaneuse, France
 

Abstract

    In this note, we show that the Onsager Machlup functional for stochastic evolution equations on a given separable Hilbert space $H$, computed in [BRT], does not depend on the closed norm considered on the functions from $[0,1]$ to $H$, dominating the norm on $L^2([0,1];H)$, and making sense for our evolution system. This extends some results of Capitaine and Lyons-Zeitouni to a wider class of norms. The main ingredient of the proof is the extension of some Gaussian correlation inequalities of Hargé and Sidak to the infinite dimensional case.

Published in: Stochastic Analysis and Applications, 21 (6), 1231-1253, 2003