Fully nonlinear stochastic pde with semilinear stochastic dependence;Équations aux dérivées partielles stochastiques complètement non linéaires avec dépendance stochastique semi-linéaire

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 331, Issue 8, 2000, Pages 617-624

  Lions, Pierre Louis ^a   Souganidis, Panagiotis E ^b,c  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034666940     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(00)00583-8     Document Type: Article

References (19)

1. Bardi M., Capuzzo-Dolceta I., Optimal Control Theory and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser, Boston.
2. Bardi M., Crandall M.G., Evans L.C., Soner H.M., Souganidis P.E., Viscosity solutions and applications, Lecture Notes in Math. 1660, Springer-Verlag, 1997.
3. Barles G., Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques et Applications 17, Springer-Verlag, 1994.
4. Chueshov I.D., Vuillermot P.-A., On a large-time dynamics of a class of random parabolic equations, C. R. Acad. Sci. Paris, Série I 322 (1996) 1181-1186.
5. Chueshov I.D., Vuillermot P.-A., On a large-time dynamics of a class of random parabolic equations subjected to homogeneous white noise: Stratonovitch's case, C. R. Acad. Sci. Paris, Série I 323 (1996) 29-33.
6. Crandall M.G., Ishii H., Lions P.-L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992) 1-67.
7. Crandall M.G., Lions P.-L., Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983) 1-42.
8. Fleming W.H., Soner H.M., Controlled Markov Processes and Viscosity Solution, Springer-Verlag, 1993.
9. Kushner H., Huang H., Limits of parabolic partial differential equations with wide band stochastic coefficients and an application to filtering theory, Stochastics 14 (1990) 115-148.
10. Lions P.-L., Souganidis P.E., Fully nonlinear stochastic partial differential equations, C. R. Acad. Sci. Paris, Série I 326 (1998) 1085-1092.
11. Lions P.-L., Souganidis P.E., Fully nonlinear stochastic partial differential equations: Nonsmooth equations and applications, C. R. Acad. Sci. Paris, Série I 327 (1998) 735-741.
12. Lions P.-L., Souganidis P.E., Équations aux Dérivées Partielles Stochastiques Non Linéaires et Solutions de Viscosité, Preprint.
13. Lions P.-L., Souganidis P.E., Uniqueness of Weak Solutions of Fully Nonlinear Stochastic pde, Preprint.
14. Mueller C., Sowers R., Blow-up for the Heat Equation with a Noise Term, Preprint.
15. Mueller C., Tribe R., A Stochastic pde Arising as the Limit of Long-range Contact Process and its Phase Transition, Preprint.
16. Pardoux E., Équations aux Dérivées Partielles Stochastiques Non Linéaires Monotones, Étude de Solutions Fortes de Type Ito, Thèse, Université Paris-Nord, 1975.
17. Pardoux E., Equations of nonlinear filtering and application to stochastic control with partial observation, CIME Course, Lecture Notes in Math. 972, Springer-Verlag, 1975.
18. Pardoux E., Stochastic partial differential equations and filtering of diffusion processes, Stochastics 3 (1979) 127-167.
19. Watanabe H., On the convergence of partial differential equations of parabolic type with rapidly oscillating coefficients to stochastic partial differential equations, Appl. Math. Optim. 20 (1989) 81-96.