Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor

Mariko Arisawa

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 4, page 415-438
  • ISSN: 0294-1449

How to cite

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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 14.4 (1997): 415-438. <http://eudml.org/doc/78417>.

@article{Arisawa1997,
author = {Arisawa, Mariko},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Hamilton-Jacobi-Bellman equations; ergodic attractor; viscosity solution},
language = {eng},
number = {4},
pages = {415-438},
publisher = {Gauthier-Villars},
title = {Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor},
url = {http://eudml.org/doc/78417},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Arisawa, Mariko
TI - Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 4
SP - 415
EP - 438
LA - eng
KW - Hamilton-Jacobi-Bellman equations; ergodic attractor; viscosity solution
UR - http://eudml.org/doc/78417
ER -

References

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  1. [1] V.I. Arnold and A. Avez, Problèmes ergodiques de la mécanique classique, Gauthier-Villars, Paris, 1967. Zbl0149.21704MR209436
  2. [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. Zbl0736.35023MR1090787
  3. [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. Zbl0635.35020MR880402
  4. [4] 1. Capuzzo-Dolcetta and P.L. Lions, Hamilton-Jacobi equations with state constraints, Trans. Amer. Math. Soc., Vol. 318, 1990, pp. 643-683. Zbl0702.49019MR951880
  5. [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. MR935395
  6. [6] I.P. Cornfeld, S.V. Fomin and Ya.G. Sinai, Ergodic Theory, New York, Springer-Verlag, 1982. Zbl0493.28007MR832433
  7. [7] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., Vol. 277, 1983, pp. 1-42. Zbl0599.35024MR690039
  8. [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. Zbl0736.35044MR1082287
  9. [9] J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer-Verlag, 33rd edition, 1990. Zbl0515.34001MR1139515
  10. [10] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics, Vol. 69, Pitman, Boston, MA, 1982. Zbl0497.35001MR667669
  11. [11] P.L. Lions, Neumann type boundary conditions for Hamilmton-Jacobi equations, Duke J. Math., Vol. 52, 1985, pp. 793-820. Zbl0599.35025MR816386
  12. [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. [13] M. Robin, On some impulse control problems with Ion run average control, SIAM J. Control and Optimization, Vol. 19, 1981, pp. 333-358. Zbl0461.93062MR613099
  14. [14] B. Simon, Functional integration and quantum physics, Academic Press, 1979. Zbl0434.28013MR544188
  15. [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. Zbl0597.49023MR838056
  16. [16] R. Temam, Infinite-dimensional dynamical systems in mecanics and physics, Springer-Verlag, 1988. Zbl0662.35001MR953967

Citations in EuDML Documents

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  1. Mariko Arisawa, Ergodic problem for the Hamilton-Jacobi-Bellman equation. II
  2. Piernicola Bettiol, On ergodic problem for Hamilton-Jacobi-Isaacs equations
  3. Mariko Arisawa, Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions
  4. Piernicola Bettiol, On ergodic problem for Hamilton-Jacobi-Isaacs equations
  5. Guy Barles, Francesca Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions

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