7 Let $ X(t) t 0 be a Brownian motion with variance parameter 2 For u 0, show that E 4 X(t u) X(t)5 X(t) Therefore, for s t, E 4 X(s) X(t)5 X(t)

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Question: 7. Let $ X(t): t 0 % be a Brownian motion with variance parameter 2. For u > 0, show that E 4 X(t

7. Let $ X(t): t ≥ 0 % be a Brownian motion with variance parameter σ2. For u > 0, show that E 4 X(t + u) | X(t)5 = X(t). Therefore, for s > t, E 4 X(s) | X(t)5 = X(t).

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