
Journal of Convex Analysis 18 (2011), No. 1, 105138 Copyright Heldermann Verlag 2011 The Fitzpatrick Function  a Bridge between Convex Analysis and Multivalued Stochastic Differential Equations Aurel Rascanu (1) Dept. of Mathematics, Al. I. Cuza University, Bd. Carol I 911, Iasi, Romania (2) Mathematics Institute, Romanian Academy of Sciences, Bd. Carol I 8, Iasi, Romania aurel.rascanu@uaic.ro Eduard Rotenstein Dept. of Mathematics, Al. I. Cuza University, Bd. Carol I 911, Iasi, Romania eduard.rotenstein@uaic.ro Using the Fitzpatrick function, we characterize the solutions for different classes of deterministic and stochastic differential equations driven by maximal monotone operators (or in particular subdifferential operators) as the minimum point of a suitably chosen convex lower semicontinuous function. Such technique provides a new approach for the existence of the solutions for the considered equations. Keywords: Maximal monotone operators, Fitzpatrick function, Skorohod problem, stochastic differential equations. MSC: 60H15; 65C30, 47H05, 47H15 [ Fulltextpdf (274 KB)] for subscribers only. 