Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude (Q2714357)
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scientific article; zbMATH DE number 1604263
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude |
scientific article; zbMATH DE number 1604263 |
Statements
13 June 2001
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Williams' decomposition
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range
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three-dimensional Bessel process
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Brownian scaling
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Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude (English)
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Two different new derivations of Czaki's formula representing the law of the ratio \(1 - Q\) of the maximum of a standard Brownian bridge relative to the amplitude process, i.e. the difference between maximum and minimum, are given. One of them uses the absolute continuity of the bridge conditioned on \(\{Q\leq v\}\) and a rescaled version of two BES(3) processes issued back to back from \(v\), and running until they hit 1.
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