9.6 Consider the Brownian motion with drift Yt 5 t 1 Bt 1 x where Y0 5

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9.6 Consider the Brownian motion with drift YðtÞ 5 μt 1 σBðtÞ 1 x where Yð0Þ 5 x and b , x ,

a. Let paðxÞ denote the probability that hits a before

b. a. Show that 1 2 d2paðxÞ dx2 1 μ dpaðxÞ dx 5 0

b. Deduce that paðxÞ 5 e22μb 2 e22μx e22μb 2 e22μa

c. What is paðxÞ when μ 5 0?

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Markov Processes For Stochastic Modeling

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2nd Edition

Authors: Oliver Ibe

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9.6 Consider the Brownian motion with drift Yt 5 t 1 Bt 1 x where Y0 5

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Markov Processes For Stochastic Modeling

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