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The Brownian bridge as a flat integral

Published online by Cambridge University Press:  28 June 2011

Nigel Cutland
Nigel Cutland
Affiliation:
Department of Pure Mathematics, University of Hull, Hull HU6 7RX, England
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Extract

The family of Brownian bridge processes (ba)a∈R has a number of characterizations, the most fundamental being that ba: [0,1] → ℝ is Brownian motion conditioned to be at the point a at time 1. Equivalently, ba is a continuous process whose law Wa is that of Wiener measure conditioned on the set of paths with x1 = a. These ideas are not so easy to make precise, so that more down to earth and workable characterizations of the Brownian bridge such as the following are often used in practice (see [6] for example)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 343 - 354
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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