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Liens entre équations différentielles stochastiques et ordinaires. (French) Zbl 0359.60087


MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34F05 Ordinary differential equations and systems with randomness

References:

[1] M.F. Allain , Sur quelques types d’approximation des solutions d’Équations Différentielles Stochastiques . Thèse Doctorat 3e Cycle , Rennes , 1974 .
[2] H.J. Anderson , Local behaviour of stochastic integral equations . Trans. Amer. Math. Soc ., Vol. 164 , 1972 . Zbl 0245.60046 · Zbl 0245.60046 · doi:10.2307/1995977
[3] A. Bonami , N. El Karoui , B. Roynette et H. Reinhard , Processus de diffusion associé à un opérateur elliptique dégénéré . Ann. Inst. Henri Poincaré , Vol. VII , n^\circ 1 , 1971 , p. 31 - 80 . Numdam | MR 290456 | Zbl 0234.60094 · Zbl 0234.60094
[4] C. Doelans-Dade , On the Existence and Unicity of Solutions of Stochastic Integral Equations. Z . Wahrscheinlichkeitstheorie verw. Gebiete , t. 36 , 1976 , p. 93 - 101 . MR 413270 | Zbl 0343.60038 · Zbl 0343.60038 · doi:10.1007/BF00533992
[5] J. Dieudonné , Fondements de l’analyse moderne (I) . Gauthier-Villars , Paris , 1965 . Zbl 0189.05501 · Zbl 0189.05501
[6] H. Doss , Quelques propriétés des processus de diffusion à valeurs dans un espace de Hilbert . Thèse de Doctorat de 3e Cycle , Université Paris VI , 1975 .
[7] N. Kazamaki , Note On a stochastic integral equation . Séminaire de Probabilités VI , Université de Strasbourg . Springer-Verlag , 1972 . Numdam | MR 375462 | Zbl 0231.60046 · Zbl 0231.60046
[8] J. Pellaumail , Une nouvelle construction de l’intégrale stochastique. Société Mathématique de France , 1973 . Astérisque 9 .
[9] P.E. Frotter , On the Existence, Uniqueness, Convergence and Explosions of solutions of Systems of Stochastic Intégral Equations . A paraître. Zbl 0363.60044 · Zbl 0363.60044 · doi:10.1214/aop/1176995849
[10] D.W. Stroock and S.R.S. Varadhan , On the support of diffusion processes with applications to the strong maximum principle. 6th , Berkeley Symposium, Vol. III , 1972 . MR 397899 | Zbl 0255.60056 · Zbl 0255.60056
[11] Wong and Zakai , On the convergence of Ordinary Integrals to Stochastic Integrals . Ann. of Math. Stat. , n^\circ 36 , 1965 . Article | MR 195142 | Zbl 0138.11201 · Zbl 0138.11201 · doi:10.1214/aoms/1177699916
[12] T. Yamada , On a comparison theorem of solutions of stochastic differential equations and its application . J. Math. Kyoto Univ. , t. 13 - 3 , 1973 . Article | MR 339334 | Zbl 0277.60047 · Zbl 0277.60047
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