Infinite horizon value functions in the Wasserstein spaces

2013/10/14 by Hynd, Ryan, Kim, Hwa Kil
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.3866

Abstract

We perform a systematic study of optimization problems in the Wasserstein spaces that are analogs of infinite horizon, deterministic control problems. We derive necessary conditions on action minimizing paths and present a sufficient condition for their existence. We also verify that the corresponding generalized value functions are a type of viscosity solution of a time independent, Hamilton-Jacobi equation in the space of probability measures. Finally, we prove a special case of a conjecture involving the subdifferential of generalized value functions and their relation to action minimizing paths.

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