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On the area under a continuous time Brownian motion till its first-passage time

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, no. 19 (2005): 4097-4104

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Abstract

The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a Fokker-Planck technique. We obtain an exact expression for the area distribution for the zero drift case, and provide various asymptotic results for the nonzero drift case, emphasizing the critical nature of the behaviour in the limi...More

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