Asymptotic evolution of a stochastic control problem when the discount vanishes

Tarres, R.

Analyse des systèmes, Astérisque no. 75-76 (1980), p. 227-237

@incollection{AST_1980__75-76__227_0,
     author = {Tarres, R.},
     title = {Asymptotic evolution of a stochastic control problem when the discount vanishes},
     booktitle = {Analyse des syst\`emes},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {75-76},
     year = {1980},
     pages = {227-237},
     zbl = {0459.49012},
     mrnumber = {581718},
     language = {en},
     url = {http://www.numdam.org/item/AST_1980__75-76__227_0}
}

Tarres, R. Asymptotic evolution of a stochastic control problem when the discount vanishes, in Analyse des systèmes, Astérisque, no. 75-76 (1980), pp. 227-237. http://www.numdam.org/item/AST_1980__75-76__227_0/

References

[1] A. Bensoussan, J. L. Lions.- Applications des inéquations variationnelles en contrôle stochastique. Collection "Méthodes mathématiques de l'Informatique", n°6, DUNOD 1978. | MR 513618 | Zbl 0411.49002

[2] W. H. Fleming. - Optimal continuous-parameter stochastic control. SIAM Review, vol.11, n°4, oct. 1969, p.470-509. | Article | MR 265046 | Zbl 0192.52501

[3] W. H. Fleming, R. W. Rishel. - Deterministic and stochastic optimal control. Springer-Verlag, 1975. | Article | MR 454768 | Zbl 0323.49001

[4] A. Friedman. - Stochastic differential equations and applications. Vol.1 and 2, Academic Press 1975. | MR 494490 | Zbl 0323.60056

[5] I. I. Gikhman, A. V. Shorohod.- Stochastic differential equations. Springer-Verlag, 1972. | MR 346904

[6] H. Kushner. - Introduction to stochastic control. Holt, Rinehart and Winston 1971. | MR 280248 | Zbl 0293.93018

[7] G. S. Ladde, V. Lakshmikantham, P. T. Liu.- Differential inequalities and Ito type stochastic differential equations. Proc. "Equations différentielles et fonctionnelles non linéaires", ed. by P. Janssens, J. Mawhin, N. Rouche ; Hermann 1973. | MR 433599 | Zbl 0274.60041

[8] J. M. Lasry.- Evolution of problems of stochastic control when the discount vanishes. Cahier de Mathématiques de la Décision n°7519 ; or Thesis (Univ. Paris-Dauphine). Or Proc. "Congrés de Contrôle optimal, I.R.I.A. 1974", Lecture Notes in Economics and mathematical systems n°107, ed. by A. Bensoussan, J.L. Lions. Springer-Verlag 1975. | Zbl 0346.93049

[9] M. Metivier.- Introduction au calcul différentiel stochastique. Journées de Théorie du Contrôle, Gourette, 1974, Univ. Bordeaux I.

[10] R. Tarres. - Contrôle optimal d'une diffusion non contrainte et non explosive ; comportement lorsque le taux d'actualisation du critère intégral s'annule. Thèse de 3ème Cycle et Cahier de Math, de la Décision n°7809, Univ. Paris-Dauphine.

R. Tarres. The results containded in the thesis are summarized in a report to appear in : Proc. Workshop on stochastic control theory and stochastic differential systems, Univ. of Bonn, January 1979 ; Lecture Notes, Springer-Verlag.

[11] R. Tarres. - To appear : The generalization of the theorems contained in the present work to the $n$ -dimensional case.

[12] M. Viot.- Introduction aux problèmes de contrôle stochastique. Journées de théorie du contrôle, Seez 1975, Univ. I et II Grenoble.