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Enlargement of σ-Algebras and Compactness of Time Changes

Published online by Cambridge University Press:  20 November 2018

J. R. Baxter  and
R. V. Chacon
J. R. Baxter
Affiliation:
University of British Columbia, Vancouver, British Columbia
R. V. Chacon
Affiliation:
University of British Columbia, Vancouver, British Columbia
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 1055 - 1065
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Baxter, J. R. and Chacon, R. V., Compactness of stopping times, to appear, Z. W. verw. G.Google Scholar
2. Chacon, R. V., Potential processes, Trans. Amer. Math. Soc. 226 (1977), 39–58.Google Scholar
3. Monroe, I., On embedding right continuous martingales in Brownian motion, Ann. Math. Stat. 43 (1972), 1293–1311.Google Scholar