Optimal Transportation Problem by Stochastic Optimal Control
Preprint Series # 690
Mikami, Toshio and Thieullen, Michele Optimal Transportation Problem by Stochastic Optimal Control. (2005);
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).
|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,
|Subjects:||60-xx PROBABILITY THEORY AND STOCHASTIC PROCESSES|