Journal of Convex Analysis 18 (2011), No. 1, 105--138
Copyright Heldermann Verlag 2011
The Fitzpatrick Function - a Bridge between Convex Analysis and Multivalued Stochastic Differential Equations
(1) Dept. of Mathematics, Al. I. Cuza University, Bd. Carol I 9-11, Iasi, Romania
(2) Mathematics Institute, Romanian Academy of Sciences, Bd. Carol I 8, Iasi, Romania
Dept. of Mathematics, Al. I. Cuza University, Bd. Carol I 9-11, Iasi, Romania
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
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