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On the geometry of Lp (μ) with applications to infinite variance processes

Published online by Cambridge University Press:  09 April 2009

R. Cheng
Affiliation:
ECI Systems and Engineering 596 Lynnhaven Parkway Virginia Beach, VA 23452USA e-mail: rayc@ecihq.com
A. G. Miamee
Affiliation:
Department of Mathematics Hampton UniversityHampton, VA 23668USA e-mail: abolghassem.miamee@hamptonu.edu
M. Pourahmadi
Affiliation:
Division of Statistics Northern Illinois UniversityDeKalb, Ill. 60115USA e-mail: pourahm@math.niu.edu
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Abstract

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Some geometric properties of Lp spaces are studied which shed light on the prediction of infinite variance processes. In particular, a Pythagorean theorem for Lp is derived. Improved growth rates for the moving average parameters are obtained.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Cambanis, S., Hardin, C. D. and Weron, A., ‘Innovations and Wold decompositions of stable processes’, Probab. Theory Relat. Fields 79 (1988), 127.CrossRefGoogle Scholar
[2]Cheng, R., Miamee, A. G. and Pourahmadi, M., ‘Some extremal problems in Lp(ω)’, Proc. Amer. Math. Soc. 126 (1998), 23332340.CrossRefGoogle Scholar
[3]Köthe, G., Topological vector spaces I (Springer, New York, 1969).Google Scholar
[4]Mazzone, F. and Cuenya, H., ‘A note on metric projections’, J. Approx. Theory 81 (1995), 425428.CrossRefGoogle Scholar
[5]Miamee, A. G. and Pourahmadi, M., ‘Wold decomposition, prediction and parameterization of stationary processes with infinite variance’, Probab. Theory Relat. Fields 79 (1988), 145164.CrossRefGoogle Scholar
[6]Rajput, B. S. and Sundberg, C., ‘On some extremal problems in Hp and the prediction of Lp-harmonizable stochastic processes’, Probab. Theory Relat. Fields 99 (1994), 197210.CrossRefGoogle Scholar