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

par Chassaing, Philippe;Louchard, Guy
Référence Journal of algorithms, 44, 1, page (29-51)
Publication Publié, 2002-07

Article révisé par les pairs

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Résumé :

The reflected Brownian Bridge area Wb conditioned on its local time b at the origin was analyzed using some properties of Airy functions. A closed form expression of the Laplace transforms of Wb was given. A recurrence equation for the moments was also given that led to an efficient computation algorithm and an asymptotic form for the density f(x,b) of Wb for x↓0.