The distribution for the stopping time of Brownian motion with one barrier is well known. There is also the formula for the expectation AB, where A and -B are the barriers, A,B bigger than 0.
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1Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Jun 23 '23 at 18:08
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Sorry, I found a reference, you can delete the question. – Tristram de Piro Jun 23 '23 at 18:11