On the Hamilton-Jacobi-Bellman equations
Copyright policy )On the Hamilton-Jacobi-Bellman equations
The author considers optimal stochastic control problems and the associated Hamilton-Jacobi-Bellman equations. The heuristic argument showing that the minimal cost function satisfies the H-J-B equation is given. Then the author shows that the minimal cost function, u, is the maximum element of the set of all sub-solutions v satisfying: \(A_{\alpha}v\leq f_{\alpha}\) in \(R^ n\), for all \(\alpha\in A\) \((A_{\alpha}\) elliptic operator). Continuity and regularity results are obtained for u, which shows u satisfies the H-J-B in a \(W^{2,\infty}\)- sense. Viscosity solutions for general second order PDE are defined.
- Université Paris Cité France
- University of Paris France
- Paris Dauphine University France
Hamilton-Jacobi-Bellman equations, viscosity solutions, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, 330, Dynamic programming in optimal control and differential games, diffusion processes, Existence of generalized solutions of PDE, Probabilités et mathématiques appliquées, 510, Dynamic Programming Principle, 519, Regularity of generalized solutions of PDE, Nonlinear boundary value problems for linear elliptic equations, Viscosity solutions, Optimal stochastic control, Diffusion processes, Continuity and regularity
Hamilton-Jacobi-Bellman equations, viscosity solutions, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, 330, Dynamic programming in optimal control and differential games, diffusion processes, Existence of generalized solutions of PDE, Probabilités et mathématiques appliquées, 510, Dynamic Programming Principle, 519, Regularity of generalized solutions of PDE, Nonlinear boundary value problems for linear elliptic equations, Viscosity solutions, Optimal stochastic control, Diffusion processes, Continuity and regularity
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