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Equivalent conditions for the tightness of a sequence of continuous Hilbert valued martingales

Published online by Cambridge University Press:  22 January 2016

Michel Métivier  and
Shintaro Nakao
Michel Métivier
Affiliation:
Ecole Polytechnique, Palaiseau, France
Shintaro Nakao
Affiliation:
Department of Mathematics, Osaka University, Toyonaka, 560, Japan
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In D. Aldous gave a sufficient condition for the tightness of a sequence (Xn)n≥0 of right continuous (with left limits) processes taking their values in a separable complete metric space S. As already noted by Aldous this condition is far from being necessary when the processes Xn are not continuous. More precisely the Aldous-condition implies the left-quasi-continuity of all the weak limits of the sequence (Xn)n≥0.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 106 , June 1987 , pp. 113 - 119
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

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