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This article characterizes conjugates and subdifferentials of convex integralfunctionals over linear spaces of cadlag stochastic processes. The approach isbased on new measurability results on the Skorokhod space and new interchangerules of integral functionals that are developed in the article. The mainresults provide a general approach to apply convex duality in a variety ofoptimization problems ranging from optimal stopping to singular stochasticcontrol and mathematical finance.

Convex integral functionals of cadlag processes