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Recursive condition for positivity of the angle for multivariate stationary sequences
Author(s):
A.
Makagon;
A.
G.
Miamee;
B.
S. W.
Schröder
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1821-1825.
MSC (1991):
Primary 60G12, 60G25
MathSciNet review:
1443841
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Abstract:
In this note a recursive type condition for positivity of the angle between past and future for  -variate stationary sequences is provided. In the case  it gives a simple different proof of a result due to Solev and Tserkhtsvadze on basicity of bivariate stationary sequences.
References:
- 1.
- Fefferman, C. (1971). Characterizations of bounded mean oscillation. Bull. Amer. Math. Soc. 77, 587-588. MR 43:6713
- 2.
- Hunt, R. A., Muckenhoupt, B. and Wheeden, R. L. (1973), Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math Soc. 176, 227-251. MR 47:701
- 3.
- Makagon, A. and Salehi, H. (1989), Notes on infinite dimensional stationary sequences. Probability Theory on Vector Spaces IV, Lecture Notes in Math. 1391, Springer-Verlag, 200-238. MR 91i:60103
- 4.
- Masani, P. and Wiener, N. (1957-58), The prediction theory of multivariate stochastic processes I and II, Acta Math. 98, 111 - 150, and 99, 93 - 137. MR 20:4323; MR 20:4325
- 5.
- Miamee, A. G. (1986), On the Angle between Past and Future for Multivariate Stationary Stochastic Processes, J. Mult. Anal. 20, 205 - 219. MR 88f:60074
- 6.
- Miamee, A. G. and Pourahmadi, M. (1987), Degenerate multivariate stationary processes: Basicity, Past and Future and Autoregressive Representation, Sankhya Ser A. 49, 316-334. MR 91b:62185
- 7.
- Pousson, H. R. (1968). Systems of Toeplitz operators on
 , II, Trans. Amer. Math. Soc. 133, 527 - 536. MR 37:3377 - 8.
- Solev, V. N. and Tserkhtsvadze, K. A. (1986), A condition for a stationary vector sequence to be a basis (Russian), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 153. MR 88b:60096
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Additional Information:
A.
Makagon
Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 26668
Email:
makagon@huajai.cs.hamptonu.edu
A.
G.
Miamee
Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 26668
Email:
miamee@cs.hamptonu.edu
B.
S. W.
Schröder
Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 26668
Address at time of publication:
Program of Mathematics and Statistics, Louisiana Technical University, Ruston, Louisiana 71272
Email:
Schroder@engr.LaTech.edu
DOI:
10.1090/S0002-9939-98-04245-2
PII:
S 0002-9939(98)04245-2
Keywords:
Multivariate stationary sequence,
prediction theory,
positive angle
Received by editor(s):
April 26, 1996
Received by editor(s) in revised form:
December 4, 1996
Additional Notes:
This research was supported by ONR Grant No. N 00014 - 89 - J - 1824
The second author was supported by Army Research Office grant DAAH 04-96-1-0027
The third author was supported by ONR Grant No. N 00014 - 95 - 1 - 0660
Communicated by:
Stanley Sawyer
Copyright of article:
Copyright
1998,
American Mathematical Society
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