Brownian Excursions Revisited
There are two classical approaches to the theory of Brownian excursions. The first one goes back to Lévy. His ideas were worked out in greater detail and extended by Itô and McKean (see , , and ). Also Chung’s and Knight’s contributions are of great importance (see , , and ). In this approach the lengths of the excursions are the basic objects. In the second approach, due to Williams (see , , and ), one works with excursions having a given maximum. In both approaches Itô’s theory of excursions (see ) plays an active part (see , and ).
KeywordsBrownian Motion Local Time Transition Density Bessel Process Strong Markov Property
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