Optimal Transportation Problem by Stochastic Optimal Control
Preprint Series # 690 Mikami, Toshio and Thieullen, Michele Optimal Transportation Problem by Stochastic Optimal Control. (2005); AbstractWe 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 MongeKantorovich 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, MongeKantorovich problem, Monge problem, duality, stochastic control, HamiltonJacobiBellman pde,
value function, vanishing viscosity,
semiconvex functions.


Subjects:  60xx PROBABILITY THEORY AND STOCHASTIC PROCESSES 

ID Code:  855 

