Hostname: page-component-cb9f654ff-c75p9 Total loading time: 0 Render date: 2025-08-26T22:33:14.429Z Has data issue: false hasContentIssue false
  • English
  • Français

Tempered processes and a Riesz decomposition for some martingales in the limit

Published online by Cambridge University Press:  18 May 2009

Louis H. Blake
Louis H. Blake
Affiliation:
College of Staten Island, Cuny, New York 10301
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.

Several papers have appeared in the past few years which have explored the topic of the Riesz decomposition for amarts. Such a decomposition for amarts enjoys several special properties. See [5, p. 208–209]. While it has been proved in [6] that not every martingale in the limit has a Riesz decomposition “in the weakest form assuring uniqueness” it is the major objective of this paper to characterize a class of martingales in the limit which is strictly larger than the class of amarts but enjoys all the properties of the decomposition for amarts.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 1 , January 1981 , pp. 9 - 17
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

1.Baez-Duarte, L., An a.e. divergent martingale that converges in probability, J. Math. Anal. Appl. 36 (1971), 149–150.CrossRefGoogle Scholar
2.Blake, L. H., A note concerning the L1 convergence of a class of games which become fairer with time, Glasgow Math. J. 13 (1972), 39–41.CrossRefGoogle Scholar
3.Blake, L. H., Every amart is a martingale in the limit, J. London Math. Soc. 18 (1978), 381–384.CrossRefGoogle Scholar
4.Doob, J. L., Stochastic processes (Wiley, 1953)”.Google Scholar
5.Edgar, G. A., and Sucheston, L., Amarts: a class of asymptotic martingales, J. Multivariate Anal. 6 (1976), 193–221.CrossRefGoogle Scholar
6.Edgar, G. A., and Sucheston, L., Martingales in the limit and amarts. Proc. Amer. Math. Soc. 67 (1977), 315–319.CrossRefGoogle Scholar
7.Meyer, P. A., Probability and potentials (Waltham, Mass., 1966).Google Scholar
8.Mucci, A. G., Limits for martingale-like sequences, Pacific J. Math. 48 (1973), 197–302CrossRefGoogle Scholar
9.Mucci, A. G., Another martingale convergence theorem, Pacific J. Math. 64 (1976), 539–541.CrossRefGoogle Scholar
10.Sucheston, L. and Ghoussoub, N., A refinement of the Riesz decomposition for amarts and semiamarts, J. Multivariate Anal. 8 (1978), 146–150.Google Scholar