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A stochastic Evans-Aronsson problem. (English) Zbl 1286.93203

This paper considers a stochastic version of the Evans-Aronsson problem which itself is related to KAM theory. This stochastic modelling is related through duality to the entropy penalized generalization of the Mather problem. Some results are stated for a special class of Hamiltonian involving periodic potential functions. The smoothness of the effective Lagrangian and Hamiltonian functions are investigated.

MSC:

93E20 Optimal stochastic control
49N15 Duality theory (optimization)
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