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Given Wide Sense Stationary (WSS) processes X and Y that are ergodic to the mean and autocovariance. Under what conditions is the correlation coefficient ergodic to the mean? ie: $lim_{T->\infty} \frac{1}{T} \int_0^T X(\tau)Y(\tau) d\tau$ converges to E[X(t)Y(t)]=constant

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  • $\begingroup$ What is the signal processing context in this question? $\endgroup$
    – MBaz
    Apr 21, 2021 at 1:11
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    $\begingroup$ @MBaz Oftentimes one estimates the correlation coefficient by averaging the correlation over time. For this to be valid it must be ergodic to the mean. Knowing this allows one to know when this is fine to do. $\endgroup$
    – roobee
    Apr 21, 2021 at 1:13

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