On the area under a continuous time Brownian motion till its first-passage time
- 25 April 2005
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 38 (19) , 4097-4104
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.Keywords
All Related Versions
This publication has 19 references indexed in Scilit:
- Convex lattice polygons of fixed area with perimeter-dependent weightsPhysical Review E, 2005
- Exact Maximal Height Distribution of Fluctuating InterfacesPhysical Review Letters, 2004
- Exact asymptotic results for persistence in the Sinai model with arbitrary driftPhysical Review E, 2002
- On the distribution of Brownian areasThe Annals of Applied Probability, 1996
- Limit distributions for the Bernoulli meanderJournal of Applied Probability, 1995
- On the Distribution of the Integral of the Absolute Value of the Brownian MotionThe Annals of Applied Probability, 1993
- Random Walk Processes and their Applications in Order StatisticsThe Annals of Applied Probability, 1992
- Kac's formula, levy's local time and brownian excursionJournal of Applied Probability, 1984
- On the Supremum of a Certain Gaussian ProcessThe Annals of Probability, 1983
- On the Integral of the Absolute Value of the Pinned Wiener ProcessThe Annals of Probability, 1982