Question: Let Sn D X1 C C Xn where the Xi are independent with EXi D 0 and var .Xi / D 2.

Let Sn D X1 C    C Xn where the Xi are independent with EXi D 0 and var .Xi / D 2.

(a) Show that S2 n  n2 is a martingale.

(b) Let  D min fn W jSnj > ag. Use Theorem 5.13 to show that E  a2=2. For simple random walk 2 D 1 and we have equality.

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