Question: Let X(t) be a Gaussian process such that for all t > s 0 we have X(t) X(s) N (0, t s). Show

Let X(t) be a Gaussian process such that for all t > s ≥ 0 we have X(t) −X(s) ∼ N (0, t −s).

Show that X(t) is mean-square continuous at any time t ≥ 0.

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