On stopping times \(T\) independent of the position \(B_T\) of a Brownian motion \((B_u, u\geqq 0)\) (Q2778350)
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scientific article; zbMATH DE number 1719879
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On stopping times \(T\) independent of the position \(B_T\) of a Brownian motion \((B_u, u\geqq 0)\) |
scientific article; zbMATH DE number 1719879 |
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20 May 2002
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stopping time
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Brownian motion
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exponential martingale
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Wald's equation
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On stopping times \(T\) independent of the position \(B_T\) of a Brownian motion \((B_u, u\geqq 0)\) (English)
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Several examples of two-dimensional random variables \((B_T, T)\), where \(B=(B_t)_{t \geq 0}\) is a Brownian motion and \(T\) is a stopping time such that \(T\) and \(B_T\) are independent, are considered. For such pairs, the law of \(T\) determines the law of \(B_T\) and vice versa. The constraints of these laws induced by the independence assumptions are studied.
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