Summary
Let (Ω,ℐ, P) be a measurable space, and {ℐ t} be a filtration on (Ω,ℐ). Then, given a fixed honest timeL a new filtrationG t} is defined, the smallest containing {ℐ t} and for whichL is a stopping time, and the martingales, semimartingales and stopping times of this new filtration are characterised.
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References
Azéma, J.: Quelques applications de la théorie générale des processus. I. Invent. Math.18, 293–336 (1972)
Dellacherie, C.: Capacités et processus stochastiques. Berlin-Heidelberg-New York: Springer 1972
Dellacherie, C., Meyer, P.A.: Probabilités et potentiel. Hermann: Paris 1975
Jacod, J.: Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete31, 235–253 (1975)
Jacod, J.: Un théorème de representation pour les martingales discontinues. Z. Wahrscheinlichkeitstheorie verw. Gebiete34, 225–244 (1976)
Jacod, J.: A general theorem of representation for martingales. Proc. Sympos. Pure Math.31, 37–53 (1977)
Jacod, J., Yor, M.: Étude des solutions extrémales et représentation intégrale des solutions pour certains problèmes de martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete38, 83–125 (1977)
Jeulin, T., Yor, M.: Grossissement d'une filtration et semi-martingales: formules explicites. Sém. Probab. Strasbourg XII, Lect. Notes Math. 649. Berlin-Heidelberg-New York: Springer 1978
Meyer, P.A.: Un cours sur les integrales stochastiques. Sém. Probab. Strasbourg X, Lect. Notes Math. 511. Berlin-Heidelberg-New York: Springer 1976
Meyer, P.A., Smythe, R.T., Walsh, J.B.: Birth and death of Markov processes. Proc. 6th Berkeley Sympos. Math. Statist. Probab. Univ. Calif.3, 293–305 (1972)
Millar, P.W.: Random times and decomposition theorems. Proc. Sympos. Pure Math.31, 91–103 (1977)
Stricker, C.: Quasimartingales, martingales locales, semimartingales et filtration naturelle. Z. Wahrscheinlichkeitstheorie verw. Gebiete39, 55–63 (1977)
Yor, M.: Grossissement d'une filtration et semi-martingales: theoremes generaux. Sém. Proba. Strasbourg XII, Lect. Notes Math. Berlin-Heidelberg-New York: Springer 1978
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Barlow, M.T. Study of a filtration expanded to include an honest time. Z. Wahrscheinlichkeitstheorie verw Gebiete 44, 307–323 (1978). https://doi.org/10.1007/BF01013194
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DOI: https://doi.org/10.1007/BF01013194