Wiener process between coaxal circles. Let W(t) be a Wie
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Wiener process between coaxal circles. Let W(t) be a Wiener process in the (x, y)-plane. Write z = x + iy, and suppose t
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Wiener process between coaxal circles. Let W(t) be a Wiener process in the (x, y)-plane. Write z = x + iy, and suppose that two circles A and B are determined, respectively, by the equations z ? ? z ? ? = ?a, z ? ? z ? ? = ?a. Suppose that W(0) = w = w1 + iw2, where w lies between A and B. Show that the probability that W(t) hits A before B is 1 log ?a ? log ?b log ww ?? ?? ? log ?a .
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