Onsager Machlup functional for stochastic evolution equations

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

We compute the Onsager Machlup functional for a stochastic evolution equation with additive noise, using $L^2$-type techniques. The regularity that has to be imposed to the drift coefficient is a trace type condition on its derivative. In the linear case, this condition does not depend on the sto- chastic convolution related to our evolution system.

Keywords: Onsager Machlup functional, estochastic evolution equation.

Published in: Annales de l'Institut Henri Poincaré, 39 (1), 69-93, 2003