PDE-viscosity solution approach to some problems of large deviations

Wendell H. Fleming; Panagiotis E. Souganidis

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1986)

  • Volume: 13, Issue: 2, page 171-192
  • ISSN: 0391-173X

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Fleming, Wendell H., and Souganidis, Panagiotis E.. "PDE-viscosity solution approach to some problems of large deviations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 13.2 (1986): 171-192. <http://eudml.org/doc/83976>.

@article{Fleming1986,
author = {Fleming, Wendell H., Souganidis, Panagiotis E.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {small random perturbation; differential game; Ventcell-Freidlin theory; small diffusion; minimum exit probability; dynamic programming},
language = {eng},
number = {2},
pages = {171-192},
publisher = {Scuola normale superiore},
title = {PDE-viscosity solution approach to some problems of large deviations},
url = {http://eudml.org/doc/83976},
volume = {13},
year = {1986},
}

TY - JOUR
AU - Fleming, Wendell H.
AU - Souganidis, Panagiotis E.
TI - PDE-viscosity solution approach to some problems of large deviations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1986
PB - Scuola normale superiore
VL - 13
IS - 2
SP - 171
EP - 192
LA - eng
KW - small random perturbation; differential game; Ventcell-Freidlin theory; small diffusion; minimum exit probability; dynamic programming
UR - http://eudml.org/doc/83976
ER -

References

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  1. [1] G. Barles, Remarques sur des resultats d'existence pour les equations de Hamilton-Jacobi du premier ordre, Annales de l'Institut H. Poincaré, Analyse Nonlinéaire, 2 (1985), pp. 21-32. Zbl0573.35010MR781590
  2. [2] M.G. Crandall - L.C. Evans - P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 282 (1984), pp. 487-502. Zbl0543.35011MR732102
  3. [3] M.G. Crandall - P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277 (1983), pp. 1-42. Zbl0599.35024MR690039
  4. [4] M.G. Crandall - P.-L. Lions - P.E. Souganidis, in preparation. 
  5. [5] M.G. Crandall - P.E. Souganidis, Developments in the theory of nonlinear first-order partial differential equations, Proc. Internat. Symp. on Differential Equations, Birmingham, Alabama (1983), Knowles and Lewis eds., North-Holland. Zbl0564.35011MR799343
  6. [6] R.J. Elliott - N.J. Kalton, The existence of value in differential games, Mem. Amer. Math. Soc., no. 126 (1972). Zbl0262.90076MR359845
  7. [7] R.J. Elliott - N.J. Kalton, Cauchy problems for certain Isaacs-Beltman equations and games of survival, Trans. Amer. Math. Soc., 198 (1974), pp. 45-72. Zbl0302.90074MR347383
  8. [8] L.C. Evans - H. Ishii, Differential games and nonlinear first-order PDE on bounded domains, Manuscripta Math., 49 (1984), pp. 109-139. Zbl0559.35013MR767202
  9. [9] L.C. Evans - H. Ishii, APDE approach to some asymptotic problems concerning random differential equations with small noise intensities, Ann. Inst. H. Poincaré, Analyses Nonlinéaire, 2 (1985), pp. 1-20. Zbl0601.60076MR781589
  10. [10] L.C. Evans - P.E. Souganidis, Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, Indiana Univ. Math. J., 33 (1984), pp. 773-797. Zbl1169.91317MR756158
  11. [11] W.H. Fleming, Exit probabilities and optimal stochastic control, Appl. Math. Optim., 4 (1978), pp. 329-346. Zbl0398.93068MR512217
  12. [12] W.H. Fleming, Stochastic control for small noise intensities, SIAM J. Control. Optim., 9 (1971), pp. 473-517. Zbl0204.47402MR304045
  13. [13] W.H. Fleming, A stochastic control approach to some large deviations problems, Springer Lecture Notes in Math., No. 1119 (1984), pp. 52-66. Zbl0585.93067MR790689
  14. [14] W.H. Fleming - P.E. Souganidis, Asymptotic series and the method of vanishing viscosity, Indiana Univ. Math. J., 35 (1986), pp. 425-447. Zbl0573.35034MR833404
  15. [15] W.H. Fleming - C.-P. Tsai, Optimal exit probabilities and differential games, Appl. Math. Optim., 7 (1981), pp. 253-282. Zbl0474.93072MR635802
  16. [16] P.-L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, 1982. Zbl0497.35001MR667669
  17. [17] P.-L. Lions - P.E. Souganidis, Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' Equations, SIAM J. Control Optim, 23 (1985), pp. 566-583. Zbl0569.49019MR791888
  18. [18] P.-L. Lions - P.E. Souganidis, Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' equations II, SIAM J. Control Optim., to appear. Zbl0628.90106
  19. [19] J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc. London, Ser. A, 264 (1969), pp. 413-496. Zbl0181.38003MR282058

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