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• W3100134655 abstract "The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a backward Fokker-Planck technique. We obtain an exact expression of the area distribution for the zero drift case, and provide various asymptotic results for the non-zero drift case, emphasising the critical nature of the behaviour in the limit of vanishing drift. The results offer important insights into the asymptotic behaviour of the area-perimeter generating functions in a class of discrete polygons. We also provide a succinct derivation for the distribution of the maximum displacement observed till the first-passage time." @default.
• W3100134655 created "2020-11-23" @default.
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• W3100134655 date "2005-04-25" @default.
• W3100134655 modified "2023-10-14" @default.
• W3100134655 title "On the area under a continuous time Brownian motion till its first-passage time" @default.
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• W3100134655 doi "https://doi.org/10.1088/0305-4470/38/19/004" @default.
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