A remark on Tsirelson's stochastic differential equation
Séminaire de probabilités de Strasbourg, Tome 33 (1999), pp. 291-303.
complété par Appendice à l’exposé précédent : « La filtration naturelle du mouvement brownien indexé par ℝ dans une variété compacte » 
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     title = {A remark on {Tsirelson's} stochastic differential equation},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {291--303},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {33},
     year = {1999},
     mrnumber = {1768002},
     zbl = {0957.60064},
     language = {en},
     url = {http://archive.numdam.org/item/SPS_1999__33__291_0/}
}
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Émery, Michel; Schachermayer, Walter. A remark on Tsirelson's stochastic differential equation. Séminaire de probabilités de Strasbourg, Tome 33 (1999), pp. 291-303. http://archive.numdam.org/item/SPS_1999__33__291_0/

[1] M. Arnaudon. Appendice à l'exposé précédent : La filtration naturelle du mouvement brownien indexé par R dans une variété compacte. In this volume. | Numdam | Zbl

[2] M.T. Barlow, M. Émery F.B. Knight, S. Song & M. Yor. Autour d'un théorème de Tsirelson sur des filtrations browniennes et non browniennes. Séminaire de Probabilités XXXII, Lecture Notes in Mathematics 1686, Springer 1998. | Numdam | Zbl

[3] S. Beghdadi-Sakrani & M. Émery. On certain probabilities equivalent to coin-tossing, d'après Schachermayer. In this volume. | Numdam | Zbl

[4] V.E. Beneš. Non existence of strong non-anticipating solutions to SDE's; implication for functional DE's, filtering and control. Stoch. Proc. Appl. 17, 243-263, 1977. | Zbl

[5] B. De Meyer. Une simplification de l'argument de Tsirelson sur le caractère non-brownien des processus de Walsh. In this volume. | Numdam | Zbl

[6] P. Diaconis. From shuffling cards to walking around the building: An introduction to modern Markov chain theory. Documenta Mathematica. Extra volume ICM 1998. I 47-64, 1998. | MR | Zbl

[7] L. Dubins, J. Feldman, M. Smorodinsky & B. Tsirelson. Decreasing sequences of σ-fields and a measure change for Brownian motion. Ann. Prob. 24, 882-904, 1996. | Zbl

[8] M. Émery & W. Schachermayer . Brownian filtrations are not stable under equivalent time-changes. In this volume. | Numdam | Zbl

[9] J. Feldman. ∈-close measures producing non-isomorphic filtrations. Ann. Prob. 24, 912-915, 1996. | MR | Zbl

[10] J. Feldman & M. Smorodinsky. Simple examples of non-generating Girsanov processes. Séminaire de Probabilités XXXI, Lecture Notes in Mathematics 1655, Springer 1997. | Numdam | Zbl

[11] J. Feldman & B. Tsirelson. Decreasing sequences of σ-fields and a measure change for Brownian motion. II Ann. Prob. 24, 905-911, 1996. | Zbl

[12] J. Kallsen. A stochastic differential equation with a unique (up to indistinguishability) but not strong solution. In this volume. | Numdam | Zbl

[13] J.-F. Le Gall and M. Yor. Sur l'équation stochastique de Tsirelson. Séminaire de Probabilités XVII, Lecture Notes in Mathematics 986, Springer 1983. | Numdam | MR | Zbl

[14] R.S. Liptser & A.N. Shiryaev. Statistics of Random Processes I. Springer, 1977. | Zbl

[15] D. Revuz & M. Yor. Continuous Martingales and Brownian Motion. Springer, 1991. | Zbl

[16] L.C.G. Rogers and D. Williams. Diffusions, Markov Processes, and Martingales. Volume 2: Itô Calculus. Wiley, 1987. | MR | Zbl

[17] W. Schachermayer. On certain probabilities equivalent to Wiener measure, d'après Dubins, Feldman, Smorodinsky and Tsirelson. In this volume. | Numdam | Zbl

[18] M. Smorodinsky. Processes with no standard extension. Israel J. Math., to appear. | MR | Zbl

[19] D.W. Stroock & M. Yor. On extremal solutions of martingale problems. Ann. Sci. École Norm. Sup. 13, 95-164, 1980. | Numdam | Zbl

[20] B. Tsirelson. Triple points: From non-Brownian filtrations to harmonic measures. GAFA, Geom. funct. anal. 7, 1096-1142, 1997. | MR | Zbl

[21] B.S. Tsirel'Son. An example of a stochastic differential equation having no strong solution. Theor. Prob. Appl. 20, 427-430, 1975. | MR | Zbl

[22] A.M. Vershik. Approximation in measure theory. Doctor Thesis, Leningrad 1973. Expanded and updated english version: The theory of decreasing sequences of measurable partitions. St. Petersburg Math. J. 6, 705-761, 1995. | Zbl

[23] J. Warren. On the joining of sticky Brownian motion. In this volume. | Numdam | Zbl

[24] H. Von Weizsäcker. Exchanging the order of taking suprema and countable intersections of σ-algebras. Ann. Inst. Henri Poincaré 19, 91-100, 1983. | Numdam | MR | Zbl

[25] D. Williams. Probability with Martingales. Cambridge University Press. 1991. | MR | Zbl

[26] M. Yor. De nouveaux résultats sur l'équation de Tsirel'son. C. R. Acad. Sci., Paris. Sér. I 309, 511-514, 1989. | MR | Zbl

[27] M. Yor. Tsirel'son's equation in discrete time. Probab. Theory Relat. Fields, 91 135-152. 1992. | MR | Zbl