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# Optimal Control for Absolutely Continuous Stochastic Processes and the Mass Transportation Problem

@inproceedings{MikamiOptimalCF, title={Optimal Control for Absolutely Continuous Stochastic Processes and the Mass Transportation Problem}, author={Toshio Mikami} }

We study the optimal control problem for R d-valued absolutely continuous stochastic processes with given marginal distributions at every time. When d = 1, we show the existence and the uniqueness of a minimizer which is a function of a time and an initial point. When d > 1, we show that a minimizer exists and that minimizers satisfy the same ordinary differential equation.