Pathwise uniqueness and approximation of solutions of stochastic differential equations

 Access to full text

 Full (PDF)

1. [1] K. Bahlali, B. Mezerdi, Y. Ouknine: Some generic properties of stochastic differential equations. Stochastics & stoch. reports, vol. 57, pp. 235-245 (1996). Zbl0892.60065
2. [2] M.T. Barlow: One dimensional stochastic differential equations with no strong solution. J. London Math. Soc. (2) 26; 335-347. Zbl0456.60062MR675177
3. [3] E. Coddington, N. Levinson: Theory of ordinary differential equations. McGraw-HillNew-york (1955). Zbl0064.33002MR69338
4. [4] J. Dieudonné: Choix d'oeuvres mathématiques. Tome 1, HermannParis (1987). 
5. [5] N. El Karoui, D. Huu Nguyen, M. Jeanblanc Piqué : Compactification methods in the control of degenerate diffusions: existence of an optimal control. Stochastics vol .20, pp.169-219 (1987). Zbl0613.60051MR878312
6. [6] M. Erraoui, Y. Ouknine: Approximation des équations différentielles stochastiques par des équations à retard. Stochastics & stoch, reports vol. 46, pp. 53-63 (1994). Zbl0826.60047
7. [7] M. Erraoui, Y. Ouknine: Sur la convergence de la formule de Lie-Trotter pour les équations différentielles stochastiques. Annales de Clermont II, série probabilités (to appear). Zbl0854.60054MR1321673
8. [8] T.C. Gard: A general uniqueness theorem for solutions of stochastic differential equations. SIAM jour. control & optim., vol. 14, 3, pp.445-457. Zbl0332.60037
9. [9] I. Gyöngy: The stability of stochastic partial differential equations and applications. Stochastics & stoch. reports, vol. 27, pp.129-150 (1989). Zbl0726.60060
10. [10] A.J. Heunis: On the prevalence of stochastic differential equations with unique strong solutions. The Annals of proba., vol. 14, 2, pp 653-662 (1986). Zbl0601.60058MR832028
11. [11] N. Ikeda, S. Watanabe: Stochastic differential equations and diffusion processes. North-Holland, Amsterdam(Kodansha Ltd, Tokyo) (1981). Zbl0495.60005MR637061
12. [12] H. Kaneko, S. Nakao : A note on approximation of stochastic differential equations. Séminaire de proba. XXII, lect. notes in math.1321, pp. 155-162. Springer verlag (1988). Zbl0647.60072MR960522
13. [13] I. Karatzas, S.E. Shreve: Brownian motion and stochastic calculus. Springer verlag, New- York Berlin Heidelberg (1988). Zbl0638.60065MR917065
14. [14] S. Kawabata: On the successive approximation of solutions of stochastic differential equations. Stochastics & stoch.reports, voL 30, pp. 69-84 (1990). Zbl0708.60051
15. [15] N.V. Krylov: Controlled diffusion processes. Springer Verlag, New- York Berlin Heidelberg (1980). Zbl0459.93002MR601776
16. [16] A. Lasota, J.A. Yorke: The generic property of existence of solutions of differential equations in Banach space. J. Diff. Equat.13 (1973), pp. 1-12. Zbl0259.34070MR335994
17. [17] S. Méléard: Martingale measure approximation, application to the control of diffusions. Prépublication du labo. de proba. , univ. Paris VI (1992). 
18. [18] W. Orlicz: Zur theorie der Differentialgleichung y' = f (z,y) . Bull. Acad. Polon. Sci. Ser. A (1932), pp. 221-228. Zbl0006.30401
19. [19] A.V. Skorokhod: Studies in the theory of random processes. Addison Wesley (1965), originally published in Kiev in (1961). Zbl0146.37701MR185620
20. [20] D.W. Strook, S.R.S. Varadhan: Mutidimensional diffusion processes. Springer VerlagBerlin (1979). 
21. [21] T. Yamada: On the successive approximation of solutions of stochastic differential equations. Jour. Math. Kyoto Univ.21 (3), pp. 501-511 (1981). Zbl0484.60053MR629781
22. [22] T. Yamada, S. Watanabe: On the uniqueness of solutions of stochastic differential equations. Jour. Math. Kyoto Univ.11 n°1, pp. 155-167 (1971). Zbl0236.60037MR278420

1. Jean-Jacques Alibert, Khaled Bahlali, Genericity in deterministic and stochastic differential equations