Dept. Math, Hokkaido Univ. EPrints Server

Optimal Transportation Problem by Stochastic Optimal Control

Preprint Series # 690
Mikami, Toshio and Thieullen, Michele Optimal Transportation Problem by Stochastic Optimal Control. (2005);

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Abstract

We solve optimal transportation problem using stochastic optimal control theory. Indeed, for a super linear cost at most quadratic at infinity, we prove Kantorovich duality theorem by a zero noise limit (or vanishing viscosity) argument. We also obtain a characterization of the support of an optimal measure in Monge-Kantorovich minimization problem (MKP) as a graph. Our key tool is a duality result for a stochastic control problem which naturally extends (MKP).

Item Type:Preprint
Additional Information:30 for us
Uncontrolled Keywords:optimal transportation, Monge-Kantorovich problem, Monge problem, duality, stochastic control, Hamilton-Jacobi-Bellman pde, value function, vanishing viscosity, semi-convex functions.
Subjects:60-xx PROBABILITY THEORY AND STOCHASTIC PROCESSES
ID Code:855