Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T23:00:19.936Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[ 1 ] Aldous, D., Stopping times and tightness, Ann. of Prob., 6, no. 2 (1978), 335–340.CrossRefGoogle Scholar
[ 2 ] Billingsley, P., Convergence of probability measures, Wiley, New York, 1968.Google Scholar
[ 3 ] Jacod, J., Mémin, J. and Métivier, M., On tightness and stopping times, Stochastic Process. Appl., 14 (1983), 109–146.CrossRefGoogle Scholar
[ 4 ] Joffe, A. and Métivier, M., Weak convergence of sequences of semimartingales with applications to multitype branching processes, Advances in Applied Probability, 18 (1986), 20–65.Google Scholar
[ 5 ] Lenglart, E., Relation de domination entre deux processus, Ann. Inst. H. Poincaré, 13, no. 2 (1977), 171–179.Google Scholar
[ 6 ] Métivier, M., Convergence faible et principe d’invariance pour des martingales à valeurs dans des espaces de Sobolev, Ann. Inst. H. Poincaré, 20, no. 4 (1984), 329–348.Google Scholar
[ 7 ] Métivier, M., Semimartingales, De Gruyter, Berlin-New York, 1982.Google Scholar
[ 8 ] Nakao, S., On weak convergence of sequences of continuous local martingales, Ann. Inst. H. Poincaré, 22, no. 3 (1986), 371–380.Google Scholar
[ 9 ] Rebolledo, R., La méthode des martingales appliquée à l’étude de la convergence en loi de processus, Mémoire de la S.M.F., t.62 (1979).CrossRefGoogle Scholar