Non-extremal martingale with Brownian filtration
DOI:
https://doi.org/10.5269/bspm.45542Resumen
Let (B_{t})_{t≥0} be the filtration of a Brownian motion (B_{t})_{t≥0} on (Ω,B,P). An example is given of an non-extremal martingale which generates the filtration (B_{t})_{t≥0}. We also discuss a property of pure martingales, we show here that it is a property of a filtration rather than a martingale.
Referencias
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14. B. Tsirelson. Triple points: from non-Brownian filtrations to harmonic measures. Geometric and Functional Analysis, 7(6):1096-1142, 1997. https://doi.org/10.1007/s000390050038
15. M. Yor. Sur l'etude des martingales continues extremales. Stochastics: An International Journal of Probability and Stochastic Processes, 2(1-4):191-196, 1979. https://doi.org/10.1080/17442507908833125
2. M. T. Barlow, M. Emery, F. B. Knight, S. Song, and M. Yor. Autour d'un theore me de tsirelson sur des filtrations Browniannes et non Browniannes. In Seminaire de Probabilites XXXII, pages 264-305. Springer, 1998. https://doi.org/10.1007/BFb0101763
3. S. Beghdadi Sakrani. Martingales continues, Filtrations faiblement Browniennes et Mesures signees. PhD thesis, Paris 6, 2000.
4. S. Beghdadi-Sakrani and M. Emery. On certain probabilities equivalent to coin-tossing, d'apres schachermayer. In Seminaire de Probabilites XXXIII, pages 240-256. Springer, 1999. https://doi.org/10.1007/BFb0096514
5. C. Dellacherie. Probabilites et potentiel: Tome 5, Processus de Markov (fin): Complements de calcul stochastique, volume 5. Hermann, 2008.
6. L. Dubins, J. Feldman, M. Smorodinsky, B. Tsirelson, et al. Decreasing sequences of sigma-fields and a measure change for Brownian motion. The Annals of Probability, 24(2):882-904, 1996. https://doi.org/10.1214/aop/1039639367
7. M. Emery and W. Schachermayer. Brownian filtrations are not stable under equivalent time-changes. Seminaire de probabilites de Strasbourg, 33:267-276, 1999. https://doi.org/10.1007/BFb0096516
8. F. B. Knight. On invertibility of martingale time changes. In Seminar on Stochastic Processes, 1987, pages 193-221. Springer, 1988. https://doi.org/10.1007/978-1-4684-0550-7_9
9. D. A. Lane. On the fields of some Brownian martingales. The Annals of Probability, pages 499-508, 1978. https://doi.org/10.1214/aop/1176995534
10. S. Laurent. On standardness and i-cosiness. In Seminaire de Probabilites XLIII, pages 127-186. Springer, 2011. https://doi.org/10.1007/978-3-642-15217-7_5
11. L. PETROVIC and D. VALJAREVI C. Statistical causality and martingale representation property with application to stochastic differential equations. Bulletin of the Australian Mathematical Society, 90(2):327-338, 2014. https://doi.org/10.1017/S000497271400029X
12. D. Revuz and M. Yor. Continuous martingales and Brownian motion, volume 293. Springer Science & Business Media, 2013.
13. D. Stroock and M. Yor. On extremal solutions of martingale problems. In Annales scientifiques de l'Ecole Normale Superieure, volume 13, pages 95-164, 1980. https://doi.org/10.24033/asens.1378
14. B. Tsirelson. Triple points: from non-Brownian filtrations to harmonic measures. Geometric and Functional Analysis, 7(6):1096-1142, 1997. https://doi.org/10.1007/s000390050038
15. M. Yor. Sur l'etude des martingales continues extremales. Stochastics: An International Journal of Probability and Stochastic Processes, 2(1-4):191-196, 1979. https://doi.org/10.1080/17442507908833125
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2022-01-24
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