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AN Lp ‘COUSIN OF COBOUNDARY’ THEOREM FOR RANDOM FIELDS

Part of: Stochastic processes

Published online by Cambridge University Press:  01 August 2008

RICHARD C. BRADLEY
RICHARD C. BRADLEY*
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA (email: bradleyr@indiana.edu)
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Abstract

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It is known that for a given and a given strictly stationary sequence of random variables, the p-norms of the partial sums are bounded if and only if the sequence consists of successive differences from another strictly stationary sequence with finite p-norm. Here this is generalized to random fields, and the assumption of stationarity is relaxed. The index is included.

Keywords

cousin of coboundaryp-normrandom field

MSC classification

Secondary: 60G60: Random fields 60G10: Stationary processes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 1 , August 2008 , pp. 51 - 58
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Aaronson, J. and Weiss, B., ‘Remarks on the tightness of cocycles’, Colloq. Math. 84/85 (2000), 363–376.CrossRefGoogle Scholar
[2]Berkes, I., ‘An extension of the Komlós subsequence theorem’, Acta. Math. Hungar. 55 (1990), 103–110.CrossRefGoogle Scholar
[3]Bradley, R. C., ‘On a theorem of K. Schmidt’, Statist. Probab. Lett. 24 (1995), 9–12.CrossRefGoogle Scholar
[4]Bradley, R. C., ‘A multiplicative coboundary theorem for some sequences of random matrices’, J. Theoret. Probab. 9 (1996), 659–678.CrossRefGoogle Scholar
[5]Bradley, R. C., ‘A coboundary theorem for sums of random variables taking their values in a Banach space’, Pacific J. Math. 178 (1997), 201–224.CrossRefGoogle Scholar
[6]Leonov, V. P., ‘On the dispersion of time averages of a stationary random process’, Theory Probab. Appl. 6 (1961), 93–101.CrossRefGoogle Scholar
[7]Moore, C. C. and Schmidt, K., ‘Coboundaries and homomorphisms for nonsingular actions and a problem of H. Helson’, Proc. London Math. Soc. (3) 40 (1980), 443–475.CrossRefGoogle Scholar
[8]Robinson, E. A., ‘Sums of stationary random variables’, Proc. Amer. Math. Soc. 11 (1960), 77–79.CrossRefGoogle Scholar
[9]Schmidt, K., Cocycles on Ergodic Transformation Groups (Macmillan India, Delhi, 1977).Google Scholar