Brownian Excursion Conditioned on Its Local Time

Brownian Excursion Conditioned on Its Local Time

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Reflected Brownian Bridge Local Time Conditioned on Its Local Time at the Origin

The Brownian Excursion multi - dimensional local time density ∗

Expressions for the multi-dimensional densities of Brownian excursion 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 Galton-Watson trees.

A Vervaat-like Path Transformation for the Reeected Brownian Bridge Conditioned on Its Local Time at 0

We describe a Vervaat-like path transformation for the reeected Brownian bridge conditioned on its local time at 0: up to random shifts, this process equals the two processes constructed from a Brownian bridge and a Brownian excursion by adding a drift and then taking the excursions over the current minimum. As a consequence, these three processes have the same occupation measure, which is easi...