Durbin, J.; (1985) The first-passage density of a continuous Gaussian process to a general boundary. **Journal of Applied Probability** , 22 (1) pp. 99-122.

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## Abstract

Under mild conditions an explicit expression is obtained for the first-passage density of sample paths of a continuous Gaussian process to a general boundary. Since this expression will usually be hard to compute, an approximation is given which is computationally simple and which is exact in the limit as the boundary becomes increasingly remote. The integral of this approximating density is itself approximated by a simple formula and this also is exact in the limit. A new integral equation is derived for the first-passage density of a continuous Gaussian Markov process. This is used to obtain further approximations.

Type: | Article |
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Title: | The first-passage density of a continuous Gaussian process to a general boundary |

Publisher version: | http://www.appliedprobability.org/content.aspx?Group=journals&Page=apjournals |

Language: | English |

Keywords: | Brownian motion, continuous Markov process, boundary-crossing probability, exit density, Volterra integral equation of the second kind |

UCL classification: | UCL > School of Arts and Social Sciences > Faculty of Social and Historical Sciences > Economics |

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