Abstract
We consider a planar Brownian motion starting from O at time t = 0 and stopped at t = 1 and a set F = {OIi; i = 1, 2, ..., n} of n semi-infinite straight lines emanating from O. Denoting by g the last time when F is reached by the Brownian motion, we compute the probability law of g. In particular, we show that, for a symmetric F and even n values, this law can be expressed as a sum of arcsin or (arcsin)2 functions. The original result of Levy is recovered as the special case n = 2. A relation with the problem of reaction–diffusion of a set of three particles in one dimension is discussed.
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