Let (Kleft(t, t^{prime}ight)=sigma^{2} exp left(-left|t-t^{prime}ight| / lambdaight)) be the scaled exponential covariance, and let (Y) be a
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Let \(K\left(t, t^{\prime}ight)=\sigma^{2} \exp \left(-\left|t-t^{\prime}ight| / \lambdaight)\) be the scaled exponential covariance, and let \(Y\) be a zero-mean Gaussian process with covariance \(K\). Show that the longrange limit with \(\sigma^{2} \propto \lambda\) is such that the deviation \(Y(t)-Y(0)\) is finite and equal in distribution to Brownian motion.
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