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Second-order approximations to the density, mean and variance of Brownian first-exit times. (English) Zbl 0567.62068

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.
Reviewer: R.A.Khan

MSC:

62L10 Sequential statistical analysis
60G40 Stopping times; optimal stopping problems; gambling theory
60J65 Brownian motion
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