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Weak law of large numbers for almost periodically correlated processes
Author(s):
A.
Makagon;
A.
G.
Miamee
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1899-1902.
MSC (1991):
Primary 60G12, 60F05
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Abstract:
This note contains two simple observations concerning the weak law of large numbers for almost periodically correlated processes.
References:
- 1.
- Cambanis, S. C., Houdre, C. L., Hurd, H. L., Leskow, J. (1994). Laws of Large Numbers for Periodically and Almost Periodically Correlated Processes, Stoch. Processes and their Appl. 53, 37-54. CMP 94:17
- 2.
- Dehay, D. Spectral Analysis of the Covariance Kernel of the of Almost Periodically Correlated Processes. Preprint.
- 3.
- Gladyshev, E. (1963). Periodically and almost periodically correlated random processes with continuous time. Th. Probab.Appl. 8, 173-177. MR 27:1986
- 4.
- Hurd, H. L. (1991). Correlation Theory of Almost Periodically Correlated Processes. J. Mult. Analysis 37, 24-45. MR 92e:60074
- 5.
- Hurd, H. L. (1992). Almost Periodically Unitary Stochastic Processes. Stoch. Processes and their Appl. 43, 99-113. MR 94g:60068
- 6.
- Hurd, H. L., Leskow, J. (1992). Estimation of the Fourier coefficients and their spectral densities for
-mixing almost periodically correlated processes. Statistics and Prob. Letters 14, 299-306. MR 93h:62172 - 7.
- Hurd, H. L., Leskow, J. (1992). Strongly consistent and asymptotically normal estimation of the covarianvce for almost periodically correlated stochastic processes. Statistics and Decision 10, 201-225. MR 94d:62213
- 8.
- Leskow, J. (1994). Asymptotic normality of the spectral density estimator for almost periodically correlated stochastic processes. Stoch. Processes and their Appl. 52, 351-360. CMP 94:17
- 9.
- Leskow J., Weron, A. (1992). Ergodic behavior and estimation for periodically correlated processes. Statistics and Prob. Letters 15, 299-304. MR 94k:62147
- 10.
- Levitan, B. M., Zhikov, V. V. Almost periodic functions and differential equations. Cambridge Univ. Press. 1982. MR 84g:34004
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Additional Information:
A.
Makagon
Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 26668
A.
G.
Miamee
Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 26668
Email:
miamee@cs.hamptonu.edu, makagon@math1.math.hamptonu.edu
DOI:
10.1090/S0002-9939-96-03379-5
PII:
S 0002-9939(96)03379-5
Keywords:
Weak law of large numbers,
almost periodically correlated processes
Received by editor(s):
November 15, 1994
Additional Notes:
This research was supported by the Office of Naval Research Grant No. N00014-89-J-1824
Communicated by:
Richard Durrett
Copyright of article:
Copyright
1996,
American Mathematical Society
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