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Lions, Pierre-Louis

Le problème de Cauchy pour les équations de Hamilton-Jacobi-Bellman. (French) Zbl 0467.49017

Ann. Fac. Sci. Toulouse, V. Ser., Math. 3, 59-68 (1981).
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scan of Zbl 0467.49017

Cited in 4 Documents

MSC:

49K45 Optimality conditions for problems involving randomness
70H20 Hamilton-Jacobi equations in mechanics
49L20 Dynamic programming in optimal control and differential games
93E20 Optimal stochastic control

Keywords:

Hamilton-Jacobi-Bellman equations; stochastic control; Wiener process; Cauchy problem; second order elliptic operators; stochastic minimization problem; Wiener space
PDFBibTeX XMLCite
\textit{P.-L. Lions}, Ann. Fac. Sci. Toulouse, Math. (5) 3, 59--68 (1981; Zbl 0467.49017)
Full Text: DOI Numdam EuDML

References:

[1] Bensoussan, A. and Lions, P.L.. «Control of random evolutions». A paraître dans Stochastics. · Zbl 0472.93073
[2] Evans, L.C.. «A convergence theorem for solutions of nonlinear second order elliptic equations». Ind. Univ. Math. J.27 (1978), p. 875-887. · Zbl 0408.35037
[3] Evans, L.C. and Friedman, A.. «Optimal stochastic switching and the Dirichlet problem for the Bellman equations». Trans. Amer. Math. Soc.253 (1979), p. 365-389. · Zbl 0425.35046
[4] Fleming, W.H. and Rishel, R.. «Deterministic and stochastic optimal control». Springer-Verlag, (1975) New-York. · Zbl 0323.49001
[5] Krylov, N.V.. «On the uniqueness of a solution of Bellman’s equation». Math. U.S.S.R. Izv.5 (1971 ), p. 1387-1398. · Zbl 0248.35101
[6] Krylov, N.V.. «Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation». Sib. Math. Journal. Vol. 17, n° 2 (1976), p. 226-236. · Zbl 0362.35038
[7] Lions, P.L.. «Résolution de problèmes généraux de Bellman Dirichlet». Comptes RendusParis, Série A 287 (1978), p. 747-750, et Acta Mathematica (1981). · Zbl 0401.35044
[8] Lions, P.L.. «Contrôle de diffusions dans IRN». Comptes RendusParis, Série A 287 (1979) p. 339-342, et Comm. Pure Appl. Math.34 (1981), p. 121-147. · Zbl 0398.93070
[9] Lions, P.L.. «Equations de Hamilton-Jacobi-Bellman dégénérées». Comptes RendusParis, Série A 289 (1979), p. 329-332. · Zbl 0424.49014
[10] Lions, P.L.. «Some problems related to the Bellman-Dirichlet equation for two elliptic operator». Comm. P.D.E.5(7) (1980), p. 753-771. · Zbl 0435.35035
[11] Lions, P.L.. A paraître.
[12] Lions, P.L. et Menaldi, J.L.. «Problèmes de Bellman avec le contrôle dans les coefficients du plus haut degré». Comptes RendusParis, Série A 287 (1978), p. 409-412, et à paraître au SIAM J. Control Optim. · Zbl 0386.93058
[13] Nisio, M.. «Some remarks on stochastic optimal controls». Japan J. Maths. Vol. 1, n° 1 (1975), p. 159-183. · Zbl 0334.93054
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