Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor
Annales de l'I.H.P. Analyse non linéaire, Volume 14 (1997) no. 4, p. 415-438
@article{AIHPC_1997__14_4_415_0,
     author = {Arisawa, Mariko},
     title = {Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {14},
     number = {4},
     year = {1997},
     pages = {415-438},
     zbl = {0892.49015},
     mrnumber = {1464529},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1997__14_4_415_0}
}
Arisawa, Mariko. Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor. Annales de l'I.H.P. Analyse non linéaire, Volume 14 (1997) no. 4, pp. 415-438. http://www.numdam.org/item/AIHPC_1997__14_4_415_0/

[1] V.I. Arnold and A. Avez, Problèmes ergodiques de la mécanique classique, Gauthier-Villars, Paris, 1967. | MR 209436 | Zbl 0149.21704

[2] G. Barles and P.L. Lions, Fully nonlinear Neumann type boundary conditions for first-order Hamilton-Jacobi equations, Nonlinear Anal. Theory Methods Appl., Vol. 16, 1991, pp. 143-153. | MR 1090787 | Zbl 0736.35023

[3] 1. Capuzzo-Dolcetta and M.G. Garroni, Oblique derivative problems and invariant measures, Ann. Scuola Norm. Sup. Pisa, Vol. 23, 1986, pp. 689-720. | Numdam | MR 880402 | Zbl 0635.35020

[4] 1. Capuzzo-Dolcetta and P.L. Lions, Hamilton-Jacobi equations with state constraints, Trans. Amer. Math. Soc., Vol. 318, 1990, pp. 643-683. | MR 951880 | Zbl 0702.49019

[5] I. Capuzzo-Dolcetta and J.L. Menaldi, On the deterministic optimal stopping time problem in the ergodic case. Theory and applications of nonlinear control system, North Holland, 1986, pp. 453-460. | MR 935395

[6] I.P. Cornfeld, S.V. Fomin and Ya.G. Sinai, Ergodic Theory, New York, Springer-Verlag, 1982. | MR 832433 | Zbl 0493.28007

[7] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., Vol. 277, 1983, pp. 1-42. | MR 690039 | Zbl 0599.35024

[8] P. Dupuis and H. Ishii, On oblique derivative problems for fully nonlinear second-order elliptic partial differential equations on non smooth domains, Nonlinear Anal. Theory Methods Appl., Vol. 15, 1990, pp. 1123-1138. | MR 1082287 | Zbl 0736.35044

[9] J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer-Verlag, 33rd edition, 1990. | MR 1139515 | Zbl 0515.34001

[10] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics, Vol. 69, Pitman, Boston, MA, 1982. | MR 667669 | Zbl 0497.35001

[11] P.L. Lions, Neumann type boundary conditions for Hamilmton-Jacobi equations, Duke J. Math., Vol. 52, 1985, pp. 793-820. | MR 816386 | Zbl 0599.35025

[12] P.L. Lions and B. Perthame, Quasi-variational inequalities and ergodic impulse control, SIAM J. Control and Optimization, Vol. 24, 1986, pp. 604-615.

[13] M. Robin, On some impulse control problems with Ion run average control, SIAM J. Control and Optimization, Vol. 19, 1981, pp. 333-358. | MR 613099 | Zbl 0461.93062

[14] B. Simon, Functional integration and quantum physics, Academic Press, 1979. | MR 544188 | Zbl 0434.28013

[15] H.M. Soner, Optimal control with state-space constraint I, SIAM J. Control Optim., Vol. 24, 1986, pp. 552-562; Optimal control with state-space constraint II, SIAM J. Control Optim., Vol. 24, 1986, pp. 1110-1122. | MR 838056 | Zbl 0597.49023

[16] R. Temam, Infinite-dimensional dynamical systems in mecanics and physics, Springer-Verlag, 1988. | MR 953967 | Zbl 0662.35001