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A definition and some characteristic properties of pseudo-stopping times. (English) Zbl 1083.60035

The main aim of this paper is to present the characterization of the so-called pseudo-stopping times, and to construct further examples, using techniques of progressive enlargements of filtrations.

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60G44 Martingales with continuous parameter
60G07 General theory of stochastic processes
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[1] Azéma, J. (1972). Quelques applications de la théorie générale des processus I. Invent. Math. 18 293–336. · Zbl 0268.60068
[2] Barlow, M. T. and Yor, M. (1981). (Semi)-martingale inequalities and local times. Z. Wahrsch. Verw. Gebiete 55 237–254. · Zbl 0451.60050
[3] Brémaud, P. and Yor, M. (1978). Changes of filtration and of probability measures. Z. Wahrsch. Verw. Gebiete 45 269–295. · Zbl 0415.60048
[4] Dellacherie, C., Maisonneuve, B. and Meyer, P. A. (1992). Probabilités et Potentiel . Chapitres XVII–XXIV: Processus de Markov (fin), Compléments de calcul stochastique. Hermann, Paris.
[5] Dellacherie, C. and Meyer, P. A. (1978). A propos du travail de Yor sur les grossissements des tribus. Seminaire de Probabilites XII. Lecture Notes in Math. 649 69–78. Springer, New York. · Zbl 0378.60033
[6] Dellacherie, C. and Meyer, P. A. (1980). Probabilités et Potentiel II . Hermann, Paris. · Zbl 0464.60001
[7] Elliott, R. J., Jeanblanc, M. and Yor, M. (2000). On models of default risk. Math. Finance 10 179–196. · Zbl 1042.91038
[8] Jeanblanc, M. and Rutkowski, M. (2000). Modeling default risk: Mathematical tools. Fixed Income and Credit Risk Modeling and Management, New York Univ., Stern School of Business, Dept. Statistics and Operations Research.
[9] Jeulin, T. (1980). Semi-Martingales et Grossissements d’une Filtration. Lecture Notes in Math. 833 . Springer, New York. · Zbl 0444.60002
[10] Jeulin, T. and Yor, M. (1978). Grossissement d’une filtration et semimartingales: Formules explicites. Seminaire de Probabilites XII. Lecture Notes in Math. 649 78–97. Springer, New York. · Zbl 0411.60045
[11] Jeulin, T. and Yor, M., eds. (1985). Grossissements de Filtrations: Exemples et Applications . Lecture Notes in Math. 1118 . Springer, New York. · Zbl 0547.00034
[12] Knight, F. B. and Maisonneuve, B. (1994). A characterization of stopping times. Ann. Probab. 22 1600–1606. JSTOR: · Zbl 0816.60039
[13] Le Gall, J. F. (1984–85). Une approche élémentaire des théorèmes de décomposition de Williams. Seminaire de Probabilites XX . Lecture Notes in Math. 1204 447–464. Springer, New York. · Zbl 0604.60081
[14] Meyer, P. A. (1978). Sur un théorème de J. Jacod. Seminaire de Probabilites XII. Lecture Notes in Math. 649 57–60. Springer, New York. · Zbl 0381.60038
[15] Meyer, P. A. (1978). Convergence faible et compacité des temps d’arrêt, d’après Baxter–Chacon. Seminaire de Probabilites XII. Lecture Notes in Math. 649 411–424. Springer, New York. · Zbl 0378.60022
[16] Pitman, J. W. and Yor, M. (1981). Bessel processes and infinitely divisible laws. In Stochastic Integrals . Lecture Notes in Math. 851 285–370. Springer, New York. · Zbl 0469.60076
[17] Protter, P. E. (2003). Stochastic Integration and Differential Equations , 2nd ed. Springer, New York. · Zbl 1041.60005
[18] Revuz, D. and Yor, M. (1999). Continuous Martingales and Brownian Motion , 3rd ed. Springer, New York. · Zbl 0917.60006
[19] Rogers, C. and Williams, D. (1987). Diffusions, Markov Processes and Martingales 2 . Itô Calculus . Wiley, New York. · Zbl 0627.60001
[20] Williams, D. (2002). A non stopping time with the optional-stopping property. Bull. London Math. Soc. 34 610–612. · Zbl 1026.60049
[21] Yor, M. (1997). Some Aspects of Brownian Motion , Part II. Some Recent Martingale Problems. Birkhäuser, Basel. · Zbl 0880.60082
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