Let (X) be a (Q)-BM. Determine (operatorname{Cov}left(X_{t}^{j}, X_{s}^{k}ight)), the characteristic function of (X(t)) and the transition probability

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Let \(X\) be a \(Q\)-BM. Determine \(\operatorname{Cov}\left(X_{t}^{j}, X_{s}^{k}ight)\), the characteristic function of \(X(t)\) and the transition probability (density) of \(X(t)\).

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