Electronic Communications in Probability

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

Toshio Mikami

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We study the optimal control problem for $\mathbb{R}^d$-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 $d \gt 1$,  we show that a minimizer exists and that  minimizers satisfy the same ordinary differential equation.

Article information

Electron. Commun. Probab., Volume 7 (2002), paper no. 20, 199-213.

Accepted: 29 October 2002
First available in Project Euclid: 16 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93E20: Optimal stochastic control

Absolutely continuous stochastic process mass transportation problem Salisbury's problem Markov control zero-noise limit

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Mikami, Toshio. Optimal Control for Absolutely Continuous Stochastic Processes and the Mass Transportation Problem. Electron. Commun. Probab. 7 (2002), paper no. 20, 199--213. doi:10.1214/ECP.v7-1061. https://projecteuclid.org/euclid.ecp/1463434787

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