On striking identities about the exponential functionals of the Brownian bridge and Brownian motion (Q5933703)
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scientific article; zbMATH DE number 1604378
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On striking identities about the exponential functionals of the Brownian bridge and Brownian motion |
scientific article; zbMATH DE number 1604378 |
Statements
On striking identities about the exponential functionals of the Brownian bridge and Brownian motion (English)
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22 June 2005
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Let \(\{ b(u), 0 \leq u \leq 1\}\) be a standart Brownian bridge, starting and ending at \(0\). The striking identity \(E\left[ \left( \int_0^1\exp (\alpha b(u)du\right) ^{-1}\right] =1\) for every real \(\alpha \) is explained and discussed.
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Brownian bridge
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Brownian motion
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negative moment
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