Question

Show that, if X : [0, 0) → R is a Brownian motion, then \mathbb{P}\left(\sup _{t \leq T} X_{t} \geq a\right) \leq e^{-\frac{a^{2}}{2 T}} Hint: recall that the rescalings X5(t)

= 8X5-24 of simple random walkon Z converge to Brownian motion.

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