Question: 3. Let $ X(t): t 0 % be a Brownian motion with variance parameter 2. For > 0, show that limt0 P *|X(t)|

3. Let $ X(t): t ≥ 0 % be a Brownian motion with variance parameter σ2. For ε > 0, show that limt→0 P *|X(t)| t > ε , = 1, whereas limt→∞ P *|X(t)| t > ε , = 0.

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