Wiener process

Brownian excursion

In probability theory a Brownian excursion process is a stochastic process that is closely related to a Wiener process (or Brownian motion). Realisations of Brownian excursion processes are essentially just realizations of a Wiener process selected to satisfy certain conditions. In particular, a Brownian excursion process is a Wiener process conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. BEPs are important because, among other reasons, they naturally arise as the limit process of a number of conditional functional central limit theorems. (Wikipedia).

Brownian excursion
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Related pages

Wiener process | Confluent hypergeometric function | Brownian motion | Probability theory | Brownian meander | Conditional probability | Stochastic process | Laplace transform | Brownian bridge