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Wayne State University

Numerical Analysis and Computation

Hamilton

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Full-Text Articles in Physical Sciences and Mathematics

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, Ii, Pierre-Louis Lions, José-Luis Menaldi Jan 1982

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, Ii, Pierre-Louis Lions, José-Luis Menaldi

Mathematics Faculty Research Publications

We consider the solution of a stochastic integral control problem, and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W1,∞(Ο),

where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

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Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, I, Pierre-Louis Lions, José-Luis Menaldi Jan 1982

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, I, Pierre-Louis Lions, José-Luis Menaldi

Mathematics Faculty Research Publications

We consider the solution of a stochastic integral control problem and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W1,∞(Ο),

where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

Go to article