The successive hitting times for the integrated Brownian motion (Q677671)
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scientific article; zbMATH DE number 999601
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The successive hitting times for the integrated Brownian motion |
scientific article; zbMATH DE number 999601 |
Statements
The successive hitting times for the integrated Brownian motion (English)
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26 November 1997
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Let \(B_t\) be the real Brownian motion, and \(X_t: =x+\int^t_0 (y+B_s)ds\). Set \(\tau_{n+1}: =\min \{t> \tau_n\mid X_t=0\}\) and \(\beta_n: =|B_{\tau_n} |\). The author computes the Kontorovich-Lebedev transform of \((\tau_n,\beta_n)\) in the two cases: \(\tau_0 =0\) or 1, and then deduces rather complicated formulas for the density of \((\tau_n, \beta_n)\), thereby completing an ancient article by H. P. McKean.
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hitting times
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Mellin transform
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Brownian motion
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Kontorovich-Lebedev transform
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