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For any random process \(X_{t}\), the Autocorrelation at time instants \(t_{1}\) and \(t_{2}\) is:

\(\displaystyle\mathbf{E}[X_{t_{1}}X_{t_{2}}]=\int_{\Omega}X_{t_{1}}(\alpha)X_{t_{2}}(\alpha)P(d\alpha)=\int_{\mathbb{R}^{2}}x_{1}x_{2}\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\)

where \(\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\) is a joint probability distribution.

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