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

@article{Chassaing2002ReflectedBB,
  title={Reflected Brownian Bridge area conditioned on its local time at the origin},
  author={Philippe Chassaing and Guy Louchard},
  journal={J. Algorithms},
  year={2002},
  volume={44},
  pages={29-51}
}
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.