Exact asymptotics for Boundary crossings of the brownian bridge with trend with application to the Kolmogorov test

2003 ◽  
Vol 55 (4) ◽  
pp. 849-864 ◽  
Author(s):  
Wolfgang Bischoff ◽  
Enkelejd Hashorva ◽  
Jürg Hüsler ◽  
Frank Miller
Keyword(s):  
Brownian Bridge ◽  
Exact Asymptotics ◽  
Kolmogorov Test ◽  
Boundary Crossings ◽  
Brownian Bridge With Trend

scholarly journals Boundary Crossings and Violations in Clinical Settings

2012 ◽  
Vol 34 (1) ◽  
pp. 21-24 ◽  
Author(s):  
V. K. Aravind ◽  
V. D. Krishnaram ◽  
Z. Thasneem
Keyword(s):  
Clinical Settings ◽  
Boundary Crossings

scholarly journals On the local time density of the reflecting Brownian bridge

2000 ◽  
Vol 13 (2) ◽  
pp. 125-136 ◽  
Author(s):  
Bernhard Gittenberger ◽  
Guy Louchard
Keyword(s):  
Limit Theorem ◽  
Local Time ◽  
Brownian Bridge ◽  
Direct Method ◽  
Random Mappings ◽  
A Direct Method ◽  
Time Density

Expressions for the multi-dimensional densities of Brownian bridge local time are derived by two different methods: A direct method based on Kac's formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings.

Approximate exit probabilities for a Brownian bridge on a short time interval, and applications

1989 ◽  
Vol 21 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. R. Lerche ◽  
D. Siegmund
Keyword(s):  
Virial Coefficient ◽  
Large Deviation ◽  
Brownian Bridge ◽  
Exit Time ◽  
Second Virial Coefficient ◽  
Dimensional Euclidean Space ◽  
Time Interval ◽  
Short Time Interval ◽  
First Exit Time ◽  
Short Time

Let T be the first exit time of Brownian motion W(t) from a region ℛ in d-dimensional Euclidean space having a smooth boundary. Given points ξ0 and ξ1 in ℛ, ordinary and large-deviation approximations are given for Pr{T < ε |W(0) = ξ0, W(ε) = ξ 1} as ε → 0. Applications are given to hearing the shape of a drum and approximating the second virial coefficient.

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