# proof of mean square convergence of the sample mean of a stationary process

$$ |

If $\gamma (n)\to 0$ as $n\to \mathrm{\infty}$ then $$, whence
$\mathrm{var}[{\overline{X}}_{n}]\to 0$.

If $$ then the dominated Convergence theorem gives

$$ |

.

Title | proof of mean square convergence of the sample mean^{} of a stationary process |
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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 |