Reflected Brownian Bridge area conditioned on its local time at the origin

Authors:
Philippe Chassaing;Guy Louchard
Affiliations:
Institut Elie Cartan, INRIA, CNRS and Université Henri Poincaré, BP 239, 54 506 Vandoeuvre cedex, France;Université Libre de Bruxelles, Département d'Informatique, CP 212, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
Venue:
Journal of Algorithms - Analysis of algorithms
Year:
2002

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Abstract

Using some properties of the Airy functions, we analyze the reflected Brownian Bridge area Wb conditioned on its local time b at the origin. We give a closed form expression of the Laplace transform of Wb, a recurrence equation for the moments, leading to an efficient computation algorithm and an asymptotic form for the density f(x, b) of Wb for x ↓ 0.