A computational approach to first-passage-time problems for Gauss–Markov processes
A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss–Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to the Brownian brid...
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| Veröffentlicht in: | Advances in applied probability 2001-06, Vol.33 (2), p.453-482 |
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| container_end_page | 482 |
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| container_start_page | 453 |
| container_title | Advances in applied probability |
| container_volume | 33 |
| creator | Di Nardo, E. Nobile, A. G. Pirozzi, E. Ricciardi, L. M. |
| description | A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss–Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to the Brownian bridge are then provided together with a comparison with some computational results by Durbin and by Daniels. Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the processes considered. |
| doi_str_mv | 10.1017/S0001867800010892 |
| format | Article |
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Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the processes considered.</description><subject>Approximation</subject><subject>Brownian bridge</subject><subject>Brownian motion</subject><subject>Covariance</subject><subject>Differential equations</subject><subject>Error rates</subject><subject>General Applied Probability</subject><subject>Markov analysis</subject><subject>Markov processes</subject><subject>Normal distribution</subject><subject>Numerical methods</subject><subject>Probability</subject><subject>Random variables</subject><subject>Series expansion</subject><subject>Studies</subject><subject>Time series</subject><issn>0001-8678</issn><issn>1475-6064</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNp1UM1Kw0AQXkTBWn0AwUPwHt3NJrubYylahYoH6zlMkklNbdy4sxW8-Q6-oU_ihhZ6EC8zzHx_zDB2LviV4EJfP3HOhVHaDJ2bPDlgI5HqLFZcpYdsNKzjAT9mJ0SrMMrAHbHFJKps1288-Na-wTqCvncWqpfI26hpHfm4ByJYYuzbDqMAlmvsKGqsi2awIfr5-n4A92o_BqxCIqRTdtTAmvBs18fs-fZmMb2L54-z--lkHldSah9jKo3KJEiNZaqSWtUCuNLK8DKrteQmFGxM3mSqAVNhmWMGeVkmqcYU61yO2eXWNyS_b5B8sbIbF66gIhEiWPNMBZLYkipniRw2Re_aDtxnIXgx_K7487ugudhqVuSt2wvSxCRKBljuLKErXVsvcR_8v-kv7Hd7hw</recordid><startdate>200106</startdate><enddate>200106</enddate><creator>Di Nardo, E.</creator><creator>Nobile, A. 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| ispartof | Advances in applied probability, 2001-06, Vol.33 (2), p.453-482 |
| issn | 0001-8678 1475-6064 |
| language | eng |
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| source | JSTOR; JSTOR Mathematics & Statistics |
| subjects | Approximation Brownian bridge Brownian motion Covariance Differential equations Error rates General Applied Probability Markov analysis Markov processes Normal distribution Numerical methods Probability Random variables Series expansion Studies Time series |
| title | A computational approach to first-passage-time problems for Gauss–Markov processes |
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