The Central Limit Theorem and the Strong Law of Large Numbers in the Spaces $l_p(x),1\leqq p < +\infty $

1977 ◽  
Vol 21 (4) ◽  
pp. 780-790 ◽  
Author(s):  
V. V. Kvartskheliya ◽  
Nguyen Xuy Tien
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
The Central Limit Theorem ◽  
Large Numbers

The estimation of frequency

1973 ◽  
Vol 10 (3) ◽  
pp. 510-519 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Sinusoidal Oscillation ◽  
Unknown Parameters ◽  
Strong Law ◽  
The Central Limit Theorem ◽  
Large Numbers

Very general forms of the strong law of large numbers and the central limit theorem are proved for estimates of the unknown parameters in a sinusoidal oscillation observed subject to error. In particular when the unknown frequency θ0, is in fact 0 or <it is shown that the estimate, , satisfies for N ≧ N0 (ω) where N0 (ω) is an integer, determined by the realisation, ω, of the process, that is almost surely finite.

The estimation of frequency

1973 ◽  
Vol 10 (03) ◽  
pp. 510-519 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Sinusoidal Oscillation ◽  
Unknown Parameters ◽  
Strong Law ◽  
The Central Limit Theorem ◽  
Large Numbers

Very general forms of the strong law of large numbers and the central limit theorem are proved for estimates of the unknown parameters in a sinusoidal oscillation observed subject to error. In particular when the unknown frequency θ 0, is in fact 0 or &lt;it is shown that the estimate, , satisfies for N ≧ N 0 (ω) where N 0 (ω) is an integer, determined by the realisation, ω, of the process, that is almost surely finite.

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