Abstract
The Brownian bridge, or tied-down Brownian motion, is derived from the standard Brownian motion on [0, 1] started at zero by constraining it to return to zero at time t = 1. A precise definition is provided and its (Gaussian) distribution is computed. The Brownian bridge arises in a wide variety of contexts. An application is given to a derivation of the Kolmogorov–Smirnov statistic in non-parametric statistics in this chapter. An application to the Hurst statistic in special topics Chapter 27, to mention a few.
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- 1.
See BCPT p.137.
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Bhattacharya, R., Waymire, E.C. (2021). The Brownian Bridge. In: Random Walk, Brownian Motion, and Martingales. Graduate Texts in Mathematics, vol 292. Springer, Cham. https://doi.org/10.1007/978-3-030-78939-8_20
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DOI: https://doi.org/10.1007/978-3-030-78939-8_20
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