Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T14:53:53.640Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Normed linear spaces and Banach spaces; Banach lattices Stochastic processes

Published online by Cambridge University Press:  09 April 2009

R. Cheng ,
A. G. Miamee  and
M. Pourahmadi
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
Rights & Permissions [Opens in a new window]

Abstract

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.

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.

MSC classification

Secondary: 60G25: Prediction theory 46B25: Classical Banach spaces in the general theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 1 , February 2003 , pp. 35 - 42
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), 1–27.CrossRefGoogle Scholar
[2]Cheng, R., Miamee, A. G. and Pourahmadi, M., ‘Some extremal problems in Lp(ω)’, Proc. Amer. Math. Soc. 126 (1998), 2333–2340.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), 425–428.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), 145–164.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), 197–210.CrossRefGoogle Scholar