Towards viscosity approximations of hierarchical fixed-point problems.

Moudafi, A.; Maingé, P.-E.

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Hierarchical convergence of a double-net algorithm for equilibrium problems and variational inequality problems.

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An implicit extragradient method for hierarchical variational inequalities.

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Potentials of a Markov process are expected suprema

Hans Föllmer, Thomas Knispel (2007)

ESAIM: Probability and Statistics

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Expected suprema of a function observed along the paths of a nice Markov process define an excessive function, and in fact a potential if vanishes at the boundary. Conversely, we show under mild regularity conditions that any potential admits a representation in terms of expected suprema. Moreover, we identify the maximal and the minimal representing function in terms of probabilistic potential theory. Our results are motivated by the work of El Karoui and Meziou (2006) on the max-plus...