Electronic Communications in Probability

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

Toshio Mikami

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463434787

Digital Object Identifier
doi:10.1214/ECP.v7-1061

Mathematical Reviews number (MathSciNet)
MR1937905

Zentralblatt MATH identifier
1030.93060

Subjects
Primary: 93E20: Optimal stochastic control

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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