Abstract
We give a concise proof, using rescaling, random time change and simple infinitesimal generator computations of the fact that Brownian excursion is the weak limit as $\varepsilon \rightarrow 0$ of tied down Brownian motion conditioned never to fall below $-\varepsilon$.
Citation
R. M. Blumenthal. "Weak Convergence to Brownian Excursion." Ann. Probab. 11 (3) 798 - 800, August, 1983. https://doi.org/10.1214/aop/1176993525
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