Problem L5.6. Let B(t) be a sBM. Consider the process Y(t) =tB(1/t), for t> 0. It is clear that Y(t) has continuous path for t> 0, and using law of large numbers, we get Y(0) = 0. It is also easy to show that Y is a Gaussian process. Prove that Cov(Y(t), Y(s)) = min(t,s). Hence, conclude that Y is a sBM.

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