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A Stochastic Analog of Aubry-Mather Theory

NONLINEARITY, no. 3 (2002): 581-603

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In this paper, we discuss a stochastic analogue of Aubry-Mather theory in which a deterministic control problem is replaced by a controlled diffusion. We prove the existence of a minimizing measure (Mather measure) and discuss its main properties using viscosity solutions of Hamilton-Jacobi equations. Then we prove regularity estimates on...更多

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