Genericity in deterministic and stochastic differential equations
Séminaire de probabilités, Tome 35 (2001), pp. 220-240 
@article{SPS_2001__35__220_0,
     author = {Alibert, Jean-Jacques and Bahlali, Khaled},
     title = {Genericity in deterministic and stochastic differential equations},
     journal = {S\'eminaire de probabilit\'es},
     pages = {220--240},
     year = {2001},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {35},
     mrnumber = {1837290},
     zbl = {0981.60062},
     language = {en},
     url = {https://www.numdam.org/item/SPS_2001__35__220_0/}
}
TY  - JOUR
AU  - Alibert, Jean-Jacques
AU  - Bahlali, Khaled
TI  - Genericity in deterministic and stochastic differential equations
JO  - Séminaire de probabilités
PY  - 2001
SP  - 220
EP  - 240
VL  - 35
PB  - Springer - Lecture Notes in Mathematics
UR  - https://www.numdam.org/item/SPS_2001__35__220_0/
LA  - en
ID  - SPS_2001__35__220_0
ER  - 
%0 Journal Article
%A Alibert, Jean-Jacques
%A Bahlali, Khaled
%T Genericity in deterministic and stochastic differential equations
%J Séminaire de probabilités
%D 2001
%P 220-240
%V 35
%I Springer - Lecture Notes in Mathematics
%U https://www.numdam.org/item/SPS_2001__35__220_0/
%G en
%F SPS_2001__35__220_0
Alibert, Jean-Jacques; Bahlali, Khaled. Genericity in deterministic and stochastic differential equations. Séminaire de probabilités, Tome 35 (2001), pp. 220-240. https://www.numdam.org/item/SPS_2001__35__220_0/

[O] W. Orlicz, (1932), Zur Theorie der Differentialgleichung y' = f(x,y), Bull. Acad. Polon. Sci. ser. A, pp. 221-228. | Zbl

[H] P. Halmos, (1944), In general a measure preserving transformation is mixing, Ann. of Math., 45, pp. 786-792. | Zbl | MR

[R] V. Rohlin, (1948), A "general" measure preserving transformation is not mixing, Dokl. Akad. Nauk. SSSR (N.S), 60, pp. 349-351. | Zbl | MR

[CL] E. Coddington, N. Levinson, (1955), Theory of ordinary differential equations, McGraw-Hill, New-York. | Zbl | MR

[S1] A.V. Skorohod, (1965), Studies in the theory of random processes, Addison-Wesley, Reading, Massachussetts. | Zbl | MR

[LL] V. Lakshmikantham and S. Leela, (1969), Differential and integral inequalities, Academic press, New York. | Zbl

[Ox] J. Oxtoby (1971), Mesure and Category, Springer, New-York.

[YW] T. Yamada, S. Watanabe, (1971). On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ. 11, 155-167. | Zbl | MR

[LY] A. Lasota, J.A. Yorke, (1973), The generic property of existence of solutions of differential equations in Banach space, J. Diff. Eq., 13, pp.1-12. | Zbl | MR

[V1] G. Vidossich, (1974), Existence and uniqueness of fixed point of non linear operators as a generic property, Bol. Soc. Brazil. Math. 5, pp. 17-29. | Zbl | MR

[V2] G. Vidossich, (1974), Most of the successive approximations do converge, J. Math. Anal. Appl., Vol. 67, N2, pp. 437-451. 45, pp. 127-131. | Zbl | MR

[DM1]F.S. De Blasi, J. Myjack, (1977), Generic properties of hyperbolic partial differential equations, J. London Math. Soc. 2, , 15, pp. 113-118. | Zbl | MR

[DM2] F.S. De Blasi, J. Myjack, (1978), Generic properties of differential equations in Banach space, Bulletin de l'Académie polonaise des sciences, série des sciences math., astr. et phys., Vol. XXVI, N 5, pp. 395-400. | Zbl | MR

[Ku] E. Kulbacka, (1978), Sur l'ensemble des points où existent les dérivées de tout ordre, Bulletin de l'Académie polonaise des sciences, série des sciences math., astr. et phys., Vol. XXVI, N 5, pp. 389-394. | Zbl | MR

[DM3] F.S. De Blasi, J. Myjack, (1979), Some generic properties of functional differential equations in Banach space, J. Math. Anal. Appl., Vol. 67, N2, pp. 437-451. | Zbl | MR

[S2] A.V. Skorohod, (1980), Stochastic differential equations dependence on a parameter, Theo. Probab. Appl., Vol. 25, N 4. | Zbl | MR

[Z] T. Zamfirescu, (1981), Most monotone functions are singular, Amer. Math. Monthly, 88, pp. 47-49. | Zbl | MR

[IW] N. Ikeda, S. Watanabe, (1981), Stochastic differential equations and diffusion processes, Amsterdam Oxford New York, North-Holland. | Zbl | MR

[KY] S. Kawabata, T. Yamada (1980/81), On some limits theorems for solutions of stochastic differential equations, Séminaire de Probabilités XVI. Lect. Notes Math., 920, Springer-Verlag, Berlin-Heidelberg. | Zbl | MR | Numdam

[He] A.J. Heunis, (1986), On the prevalence of stochastic differential equations with unique strong solutions. Ann. Probab, 14, pp. 653-662. | Zbl | MR

[KN] H. Kaneko, S. Nakao, (1988), A note on approximation for stochastic differential equations, Séminaire de Probabilités XXII. Lect. Notes. Math. 1321, pp.155-162, Berlin, Heidelberg: Springer. | Zbl | MR | Numdam

[F] X. Fernique, (1988), Un modèle presque sûr pour la convergence en loi, C.R.Acad.Sci. Paris, t. 306, Série I, p. 335-338. | Zbl | MR

[MB] E.A. Mohamed Salah, D. Bell, (1989), On the solution of stochastic ordinary differentil equations via small delay, Stoch. Stoch. Reports, Vol. 28, 4, pp. 293-299. | Zbl | MR

[EO] M. Erraoui, Y. Ouknine, (1994), Approximation des équations différentielles stochastiques par des équations à retard, Stoch. Stoch. Reports, Vol.46, pp.53-63. | Zbl | MR

[Si] B. Simon, (1995), Operators with singular continuous spectrum: I. General operators, Ann. of Math., Vol 141, pp. 131-145. | Zbl | MR

[GK] I. Gyöngy, N.V. Krylov, (1996), Existence of strong solutions for Ito's stochastic equations via approximations, Prob. Theory Relat. Fields, 105, pp. 143-158. | Zbl | MR

[BMO1] K. Bahlali, B. Mezerdi, Y. Ouknine, (1996), Some generic properties of stochastic differential equations, Stoch. Stoch. Reports. Vol.57, pp.235-245. | Zbl | MR

[BMO2] K. Bahlali, B. Mezerdi, Y. Ouknine, (1998), Pathwise uniqueness and approximations of stochastic differential Equations. Séminaire de Probabilités XXXII. Lect. Notes Math.1686, pp. 166-187, Springer-Verlag, Berlin-Heidelberg. | Zbl | MR | Numdam