@article{AIHPC_1985__2_1_1_0, author = {Evans, L. C. and Ishii, Hitoshi}, title = {A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {2}, year = {1985}, pages = {1-20}, mrnumber = {781589}, zbl = {0601.60076}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1985__2_1_1_0} }
Evans, L. C.; Ishii, H. A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities. Annales de l'I.H.P. Analyse non linéaire, Tome 2 (1985) pp. 1-20. http://gdmltest.u-ga.fr/item/AIHPC_1985__2_1_1_0/
[1] The fundamental solution of a linear parabolic equation containing a small parameter, Ill. J. Math., t. 3, 1959, p. 580-619. | MR 107758 | Zbl 0090.07601
,[2] Thèse de 3e cycle, Univ. Paris IX, Dauphine, Paris, 1983.
,[3] Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls, to appear in J. Diff. Eq. | Zbl 0548.90104
, , and ,[4] Optimal switching for ordinary differential equations, to appear in SIAM J. Control and Op., t. 22, 1984, p. 143- 161. | MR 728678 | Zbl 0641.49017
and ,[5] Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. AMS., t. 282, 1984, p. 487-502. | MR 732102 | Zbl 0543.35011
, , and ,[6] Viscosity solutions of Hamilton-Jacobi equations, Trans. AMS, t. 277, 1983, p. 1-42. | MR 690039 | Zbl 0599.35024
and ,[7] Differential games and nonlinear first-order PDE on bounded domains, to appear in Manuscripta Math. | MR 767202 | Zbl 0559.35013
, and ,[8] Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, to appear in Indiana U. Math. J. | MR 756158 | Zbl 1169.91317
and ,[9] Inclusion probability and optimal stochastic control, IRIA Seminars Review, 1977. | MR 525182
,[10] Exit probabilities and optimal stochastic control, Appl. Math. Op., t. 4, 1978, p. 329-346. | MR 512217 | Zbl 0398.93068
,[11] Logarithmic transformations and stochastic control, in Advances in Filtering and Stochastic Control (ed. by Fleming and Gorostiza), Springer, New York, 1983. | MR 794510 | Zbl 0502.93076
,[12] Stochastic Differential Equations and Applications, Vol. II, Academic Press, New York, 1976. | Zbl 0323.60057
,[13] A minimum principle for the principal eigenvalue of second order linear elliptic equations with natural boundary conditions, Comm. Pure Appl. Math., t. 31, 1978, p. 509-519. | MR 466940 | Zbl 0388.35053
,[14] Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, 1982. | MR 667669 | Zbl 1194.35459 | Zbl 0497.35001
,[15] Existence results for first-order Hamilton-Jacobi equations, to appear. | MR 740198 | Zbl 0552.70012
,[16] Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations I-III, to appear in Comm. PDE. | Zbl 0716.49022 | Zbl 0716.49023
,[17] Thesis, U. of Wisconsin, 1983.
,[18] On the behavior of the fundamental solution of the heat equation with variable coefficients, Comm. Pure Appl. Math., t. 20, 1967, p. 431-455. | MR 208191 | Zbl 0155.16503
,[19] On small random perturbations of dynamical systems, Russian Math. Surveys, t. 25, 1970, p. 1-56. | MR 267221 | Zbl 0297.34053
and ,