Another approach to the existence of value functions of stochastic differential games

Journal of Mathematical Analysis and Applications

Volumn 204, Issue 3, 1996, Pages 884-897

  Świȩch, Andrzej ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030589793     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0474     Document Type: Article

References (22)

1. 1. T. Basar and G. J. Olsder, "Dynamic Noncooperative Game Theory," Academic Press, San Diego, 1995.
2. 2. L. Caffarelli, M. G. Crandall, M. Kocan, and A. Świȩch, On viscosity solutions of fully nonlinear equations with measurable ingredients, Comm. Pure Appl. Math. 49 (1996), 365-397.
3. 3. M. G. Crandall, H. Ishii, and P. L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992), 1-67.
4. 4. R. J. Elliot and N. J. Kalton, The existence of value in differential games, Mem. Amer. Math. Soc. 126 (1972).
5. 5. L. C. Evans and P. E. Souganidis, Differential games and representation formulas for solutions of Hamilton-Jacobi equations, Indiana Univ. Math. J. 33 (1984), 773-797.
6. 6. W. H. Fleming and H. M. Soner, "Controlled Markov Processes and Viscosity Solutions," Springer-Verlag, Berlin/New York, 1993.
7. 7. W. H. Fleming and P. E. Souganidis, On the existence of value functions of two-player, zero-sum stochastic differential games, Indiana Univ. Math. J. 38 No. 2 (1989), 293-314.
8. 8. W. H. Fleming and P. E. Souganidis, Two-player, zero-sum stochastic differential games, in "Analyse Mathematique et Applications," Gauthier-Villars, Paris, 1988.
9. 9. A. Friedman, "Differential Games," Wiley, New York, 1971.
10. 10. A. Friedman, "Differential Games," CBMS-AMS Vol. 18 Providence, RI, 1974.
11. 11. R. Isaacs, "Differential Games," Wiley, New York, 1965.
12. 12. H. Ishii, On the equivalence of two notions of weak solutions, viscosity solutions and distribution solutions, Funkcialaj Ekvacioj 38 (1995), 101-120.
13. 13. H. Ishii and P. L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations 83 (1990), 26-78.
14. 14. R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Rational Mech. Anal. 101 (1988), 1-27.
15. 15. M. A. Katsoulakis, A representation formula and regularizing properties for viscosity solutions of second-order fully nonlinear degenerate parabolic equations, Nonlinear Anal. 24 (1995), 147-158.
16. 16. N. V. Krylov, "Controlled Diffusion Processes," Springer-Verlag, New York, 1980.
17. 17. P. L. Lions Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Parts 1, 2, Comm. Partial Differential Equations 8 (1983), 1101-1174 and 1229-1276.
18. 18. P. L. Lions and 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), 566-583.
19. 19. P. L. Lions and P. E. Souganidis, Viscosity solutions of second-order equations, stochastic control and stochastic differential games, in "Stochastic Differential Systems, Stochastic Control Theory and Applications" (W. H. Fleming and P. L. Lions, Eds.), IMA Vol. Math. Appl., Vol. 10, Springer-Verlag, Berlin, 1988.
20. 20. D. W. Stroock and S. R. S. Varadhan, "Multidimensional Diffusion Processes," Springer-Verlag, New York, 1979.
21. 21. A. Świȩch, Sub-and superoptimality principles of dynamic programming revisited Nonlinear Anal. 26 (1996), 1429-1436.
22. 22. A. Świȩch, The existence of value functions of stochastic differential games for unbounded stochastic evolution, Proceedings of the 34th IEEE Conference on Decision and Control, New Orleans, Louisiana, December 13-15, 1995, 2289-2294.