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On non-additive processes

Published online by Cambridge University Press:  19 September 2008

Ulrich Wacker
Ulrich Wacker
Affiliation:
Fakultät für Mathematik und Informatik der Universität Passau, Innstr. 27, D-8390 Passau, West Germany
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Abstract

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The aim of this paper is to introduce and study the class of boundedly non-additive processes. The main result is the decomposition in theorem (2.1) and theorem (3.1), which says that a boundedly non-additive process is the sum of a non-positive subadditive, a non-negative superadditive and an additive process. By this decomposition we can extend the mean and local ergodic theorems for superadditive processes of M. A. Akcoglu and U. Krengel to boundedly non-additive processes. At the end of this paper some examples are given.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985 , pp. 291 - 299
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Akcoglu, M. A. & Krengel, U.. Ergodic theorems for superadditive processes. J. Reine Ang. Math. 323 (1981), 53–67.Google Scholar
[2]Derriennic, Y.. Un theoreme ergodique presque sous-additif. Ann. Prob. 11 (1983), 669–677.CrossRefGoogle Scholar
[3]del Junco, A.. On the decomposition of a subadditive stochastic process. Ann. Prob. 5 (1981), 298–302.Google Scholar
[4]Kingman, J. F. C.. Subadditive processes. In Lecture Notes in Mathematics 539, 167–223. Springer-Verlag: Berlin-Heidelberg-New York, 1976.Google Scholar
[5]Smythe, R. T. & Wierman, J. C.. First-Passage Percolation on the Square Lattice. Lecture Notes in Mathematics 671, Springer-Verlag: Berlin-Heidelberg-New York, 1978.CrossRefGoogle Scholar