Optimal Control for Absolutely Continuous Stochastic Processes and the Mass Transportation Problem
Toshio Mikami, Hokkaido University
Abstract
We study the optimal control problem for Rd-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.
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