Second-order approximations to the density, mean and variance of Brownian first-exit times (Q1059969)
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scientific article; zbMATH DE number 3905687
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Second-order approximations to the density, mean and variance of Brownian first-exit times |
scientific article; zbMATH DE number 3905687 |
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Second-order approximations to the density, mean and variance of Brownian first-exit times (English)
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1985
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Let W be a Brownian motion with drift \(\theta\), and let \(T=\inf \{t>0:\quad W(t)\geq \psi (t)\}.\) Under suitable conditions on \(\psi\) (t) the author obtains second order approximations to the density, mean and variance of the distribution of the first exit time T. Several examples including some in connection with sequential tests are discussed.
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correction terms
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tangent approximation
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drift
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second order approximations
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mean
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variance
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distribution of the first exit time
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