Pathwise uniqueness and approximation of solutions of stochastic differential equations
Séminaire de probabilités de Strasbourg, Tome 32 (1998), pp. 166-187.
@article{SPS_1998__32__166_0,
     author = {Bahlali, Khaled and Mezerdi, Brahim and Ouknine, Youssef},
     title = {Pathwise uniqueness and approximation of solutions of stochastic differential equations},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {166--187},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {32},
     year = {1998},
     mrnumber = {1655150},
     zbl = {0910.60049},
     language = {en},
     url = {http://www.numdam.org/item/SPS_1998__32__166_0/}
}
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Bahlali, Khaled; Mezerdi, Brahim; Ouknine, Youssef. Pathwise uniqueness and approximation of solutions of stochastic differential equations. Séminaire de probabilités de Strasbourg, Tome 32 (1998), pp. 166-187. http://www.numdam.org/item/SPS_1998__32__166_0/

[1] K. Bahlali, B. Mezerdi, Y. Ouknine: Some generic properties of stochastic differential equations. Stochastics & stoch. reports, vol. 57, pp. 235-245 (1996). | Zbl

[2] M.T. Barlow: One dimensional stochastic differential equations with no strong solution. J. London Math. Soc. (2) 26; 335-347. | MR | Zbl

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

[4] J. Dieudonné: Choix d'oeuvres mathématiques. Tome 1, Hermann Paris (1987).

[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). | MR | Zbl

[6] M. Erraoui, Y. Ouknine: Approximation des équations différentielles stochastiques par des équations à retard. Stochastics & stoch, reports vol. 46, pp. 53-63 (1994). | Zbl

[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). | Numdam | MR | Zbl

[8] T.C. Gard: A general uniqueness theorem for solutions of stochastic differential equations. SIAM jour. control & optim., vol. 14, 3, pp.445-457. | Zbl

[9] I. Gyöngy: The stability of stochastic partial differential equations and applications. Stochastics & stoch. reports, vol. 27, pp.129-150 (1989). | Zbl

[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). | MR | Zbl

[11] N. Ikeda, S. Watanabe: Stochastic differential equations and diffusion processes. North-Holland, Amsterdam(Kodansha Ltd, Tokyo) (1981). | MR | Zbl

[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). | Numdam | MR | Zbl

[13] I. Karatzas, S.E. Shreve: Brownian motion and stochastic calculus. Springer verlag, New- York Berlin Heidelberg (1988). | MR | Zbl

[14] S. Kawabata: On the successive approximation of solutions of stochastic differential equations. Stochastics & stoch.reports, voL 30, pp. 69-84 (1990). | Zbl

[15] N.V. Krylov: Controlled diffusion processes. Springer Verlag, New- York Berlin Heidelberg (1980). | MR | Zbl

[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. | MR | Zbl

[17] S. Méléard: Martingale measure approximation, application to the control of diffusions. Prépublication du labo. de proba. , univ. Paris VI (1992).

[18] W. Orlicz: Zur theorie der Differentialgleichung y' = f (z,y) . Bull. Acad. Polon. Sci. Ser. A (1932), pp. 221-228. | Zbl

[19] A.V. Skorokhod: Studies in the theory of random processes. Addison Wesley (1965), originally published in Kiev in (1961). | MR | Zbl

[20] D.W. Strook, S.R.S. Varadhan: Mutidimensional diffusion processes. Springer Verlag Berlin (1979).

[21] T. Yamada: On the successive approximation of solutions of stochastic differential equations. Jour. Math. Kyoto Univ. 21 (3), pp. 501-511 (1981). | MR | Zbl

[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). | MR | Zbl