Geodesic
Enlargement of σ-Algebras and Compactness of Time Changes
Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 1055-1065

Voir la notice de l'article provenant de la source Cambridge University Press

Given a stochastic process adapted to an increasing family of right-continuous σ-algebras, it is often useful for many purposes to enlarge the a-algebras. In the present paper we shall consider enlargements which involve embedding the process in a larger probability space. The first question investigated is what kinds of enlargements it might be useful to consider. To study stopping times, the least requirement needed to have a complete theory is that convergent sequences of stopping times converge to a function which is also a stopping time, and for this it is necessary to make the enlargement right continuous. 
Baxter, J. R.; Chacon, R. V. Enlargement of σ-Algebras and Compactness of Time Changes. Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 1055-1065. doi: 10.4153/CJM-1977-102-0
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[1] 1. Baxter, J. R. and Chacon, R. V., Compactness of stopping times, to appear, Z. W. verw. G. Google Scholar

[2] 2. Chacon, R. V., Potential processes, Trans. Amer. Math. Soc. 226 (1977), 39–58. Google Scholar

[3] 3. Monroe, I., On embedding right continuous martingales in Brownian motion, Ann. Math. Stat. 43 (1972), 1293–1311. Google Scholar

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