8. Consider the random walk that in each t time unit either goes up or down the

8. Consider the random walk that in each Δt time unit either goes up or down the amount with respective probabilities p and , where .

(a) Argue that as the resulting limiting process is a Brownian motion process with drift rate μ.

(b) Using part

(a) and the results of the gambler's ruin problem (Section 4.5.1), compute the probability that a Brownian motion process with drift rate μ goes up A before going down .