1 5 32 Use the gamblers ruin formula from Problem 3 26 to make plausible that, for any c, d 0, P(process hits c before d) 1e2d 2 1 e2(d c) 2 for a Brownian motion process with drift parameter 0 and variance parameter 2 (the probability is d (d c)if 0) Remark use the fact that lim0(1 a )1 ea for any constant a

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Question: 1. 5.32 Use the gamblers ruin formula from Problem 3.26 to make plausible that, for any c, d > 0, P(process hits c before

1. 5.32 Use the gambler’s ruin formula from Problem 3.26 to make plausible that, for any

c, d > 0, P(process hits c before −

d) = 1−e−2dμ/σ2 1 −e−2(d+c)μ/σ2 for a Brownian motion process with drift parameter μ= 0 and variance parameter σ2 (the probability is d/(d + c)ifμ = 0). Remark: use the fact that lim→0(1 +
a )1/ = ea for any constant a.

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