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Optimal control of reflected diffusion processes : An example of state constraints

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Stochastic Differential Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 78))

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References

  1. A. Bensoussan: Stochastic control by functional analysis methods. North-Holland, Amsterdam, 1982.

    Google Scholar 

  2. A. Bensoussan and J.L. Lions: Applications des inéquations variationnelles en contrôle stochastique, Dunod, Paris, 1976.

    Google Scholar 

  3. A. Bensoussan and J.L. Lions: Contrôle impulsionnel et inéquations quasivariationnelles, Dunod, Paris, 1982.

    Google Scholar 

  4. M.G. Crandall, L.C. Evans and P.L. Lions: Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 282 (1984), p. 487–502.

    Google Scholar 

  5. M.G. Crandall and P.L. Lions: Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 277 (1983), p. 1–42. Announced in C.R. Acad. Sci. Paris, 292 (1981), p. 183–186.

    Google Scholar 

  6. M.G. Crandall and P.L. Lions: Hamilton-Jacobi equations in infinite dimensions. Part I, J. Funct. Anal. (1985); Part II, to appear in J. Funct. Anal. Announced in C.R. Acad. Sci. Paris, 300 (1985). p. 67–70.

    Google Scholar 

  7. W.H. Fleming and R. Rishel: Deterministic and stocahstic optimal sontrol, Springer, Berlin, 1975.

    Google Scholar 

  8. F. Gimbert: Problèmes de Neumann quasilinéaires ergodiques. J. Funct. Anal.

    Google Scholar 

  9. F. Gimbert and P.L. Lions: Existence and regularity results for solutions of second-order, elliptic, integrodifferential operators. To appear in Ric. Mat. Napoli.

    Google Scholar 

  10. I. Capuzzo-Dolcetta and P.L. Lions: work in preparation.

    Google Scholar 

  11. M. Kohlmann: Viscosity solutions in partially observed control. Preprint.

    Google Scholar 

  12. N.V. Krylov: Controlled diffusion processes. Springer, Berlin, 1980.

    Google Scholar 

  13. J.M. Lasry and P.L. Lions: work in preparation. Announced in C.R. Acad. Sci. Paris.

    Google Scholar 

  14. P.L. Lions: Optimal stochastic control with state constraints. In "Stochastic Differential Systems", Lecture Notes in Control and Information Sciences, 69, Springer, Berlin, 1985.

    Google Scholar 

  15. P.L. Lions: Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Parts 1, 2, Comm. P.D.E., 8 (1983), p. p. 1101–1174 and p. 1229–1276; Part 3, In Nonlinear Partial Differential equations and their applications. Collège de France Seminar, Vol. V, Pitman, London, 1983.

    Google Scholar 

  16. P.L. Lions: On the Hamilton-Jacobi-Bellman equations. Acta Applicandae, 1 (1983), p. 17–41.

    Google Scholar 

  17. P.L. Lions: Some recent results in the optimal control of diffusion processes. Stochastic analysis, Proc. of the Taniguchi Intern. Symp. on Stochastic Analysis, Katata and Kyoto, 1982; Kinokuniga, Tokyo (1984).

    Google Scholar 

  18. P.L. Lions: Neumann type boundary conditions for Hamilton-Jacobi equations. Duke Math. J..

    Google Scholar 

  19. P.L. Lions: Generalized solutions of Hamilton-Jacobi equations. Pitman, London, 1982.

    Google Scholar 

  20. P.L. Lions: Quelques remarques sur les problèmes elliptiques quasilinéaires du second ordre. J. Analyse Math..

    Google Scholar 

  21. P.L. Lions and B. Perthame: Quasi-variational inequalities and ergodic impulse control. SIAM J. Control Optim..

    Google Scholar 

  22. P.L. Lions and A.S. Sznitman: Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math., 37 (1984), p. 511–537.

    Google Scholar 

  23. P.L. Lions and N.S. Trudinger: Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equation.

    Google Scholar 

  24. P.L. Lions and N.S. Trudinger: Optimal control of reflected diffusion processes with optimal stopping. Preprint.

    Google Scholar 

  25. B. Perthame and R. Sanders: The Neumann problem for fully nonlinear second-order singular perturbation problems. M.R.C. report.

    Google Scholar 

  26. M. Soner: Optimal control with state-space constraint. I. Preprint.

    Google Scholar 

  27. N.S. Trudinger: to appear.

    Google Scholar 

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Authors and Affiliations

  1. Ceremade, Université Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cedex 16

    P. L. Lions

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  1. P. L. Lions
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Norbert Christopeit Kurt Helmes Michael Kohlmann

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© 1986 Springer-Verlag

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Lions, P.L. (1986). Optimal control of reflected diffusion processes : An example of state constraints. In: Christopeit, N., Helmes, K., Kohlmann, M. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0041170

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  • DOI: https://doi.org/10.1007/BFb0041170

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16228-5

  • Online ISBN: 978-3-540-39767-0

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