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- W2001822012 abstract "Let ( B s ) s≥t be Brownian motion, t be the starting moment, B t = x , EB s = x , DB s = s – t . Let T ≥ t be a fixed time-horizon, and lower( s ), upper( s ) be two smooth real functions, defined for s ∈ [ t ; T ], such that lower( s ) < upper( s ) for all s ∈ [ t ; T ), lower( t ) ≤ x ≤ upper ( t ). Finally, let τ = inf { s ∈ [ t ; T )| B s = lower( s ) or B s = upper( s )}, where inf ø = T , and let = {B τ = upper( τ )}, = { B τ = lower( τ )}, . We obtain explicit formulae for P t, x (), P t, x (), and P t, x () in two special cases: square-root boundaries with a natural horizon and arcsine boundaries with no horizon." @default.
- W2001822012 created "2016-06-24" @default.
- W2001822012 creator A5035819244 @default.
- W2001822012 date "2008-01-01" @default.
- W2001822012 modified "2023-10-18" @default.
- W2001822012 title "Levels of crossing probability for Brownian motion" @default.
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- W2001822012 doi "https://doi.org/10.1515/rose.2008.005" @default.
- W2001822012 hasPublicationYear "2008" @default.
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