proof of mean square convergence of the sample mean of a stationary process
nvar(ˉXn)=1nn∑i=1n∑j=1cov(Xi,Xj)=∑|h|<n(1-|h|n)γ(h)≤∑|h|<n|γ(h)| |
If γ(n)→0 as n→∞ then lim, whence
.
If then the dominated Convergence theorem gives
.
Title | proof of mean square convergence of the sample mean![]() |
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Canonical name | ProofOfMeanSquareConvergenceOfTheSampleMeanOfAStationaryProcess |
Date of creation | 2013-03-22 15:22:19 |
Last modified on | 2013-03-22 15:22:19 |
Owner | georgiosl (7242) |
Last modified by | georgiosl (7242) |
Numerical id | 6 |
Author | georgiosl (7242) |
Entry type | Proof |
Classification | msc 60G10 |