@article{SPS_1999__33__291_0,
author = {\'Emery, Michel and Schachermayer, Walter},
title = {A remark on {Tsirelson's} stochastic differential equation},
journal = {S\'eminaire de probabilit\'es},
pages = {291--303},
year = {1999},
publisher = {Springer - Lecture Notes in Mathematics},
volume = {33},
mrnumber = {1768002},
zbl = {0957.60064},
language = {en},
url = {https://www.numdam.org/item/SPS_1999__33__291_0/}
}
TY - JOUR AU - Émery, Michel AU - Schachermayer, Walter TI - A remark on Tsirelson's stochastic differential equation JO - Séminaire de probabilités PY - 1999 SP - 291 EP - 303 VL - 33 PB - Springer - Lecture Notes in Mathematics UR - https://www.numdam.org/item/SPS_1999__33__291_0/ LA - en ID - SPS_1999__33__291_0 ER -
Émery, Michel; Schachermayer, Walter. A remark on Tsirelson's stochastic differential equation. Séminaire de probabilités, Tome 33 (1999), pp. 291-303. https://www.numdam.org/item/SPS_1999__33__291_0/
[1] . Appendice à l'exposé précédent : La filtration naturelle du mouvement brownien indexé par R dans une variété compacte. In this volume. | Zbl | Numdam
[2] , , & . Autour d'un théorème de Tsirelson sur des filtrations browniennes et non browniennes. Séminaire de Probabilités XXXII, Lecture Notes in Mathematics 1686, Springer 1998. | Zbl | Numdam
[3] & . On certain probabilities equivalent to coin-tossing, d'après Schachermayer. In this volume. | Zbl | Numdam
[4] . 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] . Une simplification de l'argument de Tsirelson sur le caractère non-brownien des processus de Walsh. In this volume. | Zbl | Numdam
[6] . 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. | Zbl | MR
[7] , , & . Decreasing sequences of σ-fields and a measure change for Brownian motion. Ann. Prob. 24, 882-904, 1996. | Zbl
[8] & . Brownian filtrations are not stable under equivalent time-changes. In this volume. | Zbl | Numdam
[9] . ∈-close measures producing non-isomorphic filtrations. Ann. Prob. 24, 912-915, 1996. | Zbl | MR
[10] & . Simple examples of non-generating Girsanov processes. Séminaire de Probabilités XXXI, Lecture Notes in Mathematics 1655, Springer 1997. | Zbl | Numdam
[11] & . Decreasing sequences of σ-fields and a measure change for Brownian motion. II Ann. Prob. 24, 905-911, 1996. | Zbl
[12] . A stochastic differential equation with a unique (up to indistinguishability) but not strong solution. In this volume. | Zbl | Numdam
[13] and . Sur l'équation stochastique de Tsirelson. Séminaire de Probabilités XVII, Lecture Notes in Mathematics 986, Springer 1983. | Zbl | MR | Numdam
[14] & . Statistics of Random Processes I. Springer, 1977. | Zbl
[15] & . Continuous Martingales and Brownian Motion. Springer, 1991. | Zbl
[16] and . Diffusions, Markov Processes, and Martingales. Volume 2: Itô Calculus. Wiley, 1987. | Zbl | MR
[17] . On certain probabilities equivalent to Wiener measure, d'après Dubins, Feldman, Smorodinsky and Tsirelson. In this volume. | Zbl | Numdam
[18] . Processes with no standard extension. Israel J. Math., to appear. | Zbl | MR
[19] & . On extremal solutions of martingale problems. Ann. Sci. École Norm. Sup. 13, 95-164, 1980. | Zbl | Numdam
[20] . Triple points: From non-Brownian filtrations to harmonic measures. GAFA, Geom. funct. anal. 7, 1096-1142, 1997. | Zbl | MR
[21] . An example of a stochastic differential equation having no strong solution. Theor. Prob. Appl. 20, 427-430, 1975. | Zbl | MR
[22] . 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] . On the joining of sticky Brownian motion. In this volume. | Zbl | Numdam
[24] . Exchanging the order of taking suprema and countable intersections of σ-algebras. Ann. Inst. Henri Poincaré 19, 91-100, 1983. | Zbl | MR | Numdam
[25] . Probability with Martingales. Cambridge University Press. 1991. | Zbl | MR
[26] . De nouveaux résultats sur l'équation de Tsirel'son. C. R. Acad. Sci., Paris. Sér. I 309, 511-514, 1989. | Zbl | MR
[27] . Tsirel'son's equation in discrete time. Probab. Theory Relat. Fields, 91 135-152. 1992. | Zbl | MR






