Exact formulas for the moments of the first passage time of reward processes
Let {Zρ(t), t ≥ 0} be a reward process based on a semi-Markov process {J (t), t ≥ 0} and a reward function ρ. Let Tz be the first passage time of {Zρ(t), t ≥ 0} from Zρ(0) = 0 to a prespecified level z. In this article we provide the Laplace transform of the E[T k z ] and obtain the exact formulas...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2005-06-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/17 |
| _version_ | 1817997000461778944 |
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| author | G.A. Parham |
| author_facet | G.A. Parham |
| author_sort | G.A. Parham |
| collection | DOAJ |
| description |
Let {Zρ(t), t ≥ 0} be a reward process based on a semi-Markov process {J (t), t ≥ 0} and a reward function ρ. Let Tz be the first passage time of {Zρ(t), t ≥ 0} from Zρ(0) = 0 to a prespecified level z. In this article we provide the Laplace transform of the E[T k z ] and obtain the exact formulas for ETz, ET 2 z and var(Tz). Formulas for certain type I counter models are given.
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| first_indexed | 2024-04-14T02:31:47Z |
| format | Article |
| id | doaj.art-10b299d8fca74e91a018345e260fbb2b |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T02:31:47Z |
| publishDate | 2005-06-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-10b299d8fca74e91a018345e260fbb2b2022-12-22T02:17:39ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712005-06-013110.57805/revstat.v3i1.17Exact formulas for the moments of the first passage time of reward processesG.A. Parham0Shahid Chamran University Let {Zρ(t), t ≥ 0} be a reward process based on a semi-Markov process {J (t), t ≥ 0} and a reward function ρ. Let Tz be the first passage time of {Zρ(t), t ≥ 0} from Zρ(0) = 0 to a prespecified level z. In this article we provide the Laplace transform of the E[T k z ] and obtain the exact formulas for ETz, ET 2 z and var(Tz). Formulas for certain type I counter models are given. https://revstat.ine.pt/index.php/REVSTAT/article/view/17semi-Markov processreward processLaplace transformfirst passage time |
| spellingShingle | G.A. Parham Exact formulas for the moments of the first passage time of reward processes Revstat Statistical Journal semi-Markov process reward process Laplace transform first passage time |
| title | Exact formulas for the moments of the first passage time of reward processes |
| title_full | Exact formulas for the moments of the first passage time of reward processes |
| title_fullStr | Exact formulas for the moments of the first passage time of reward processes |
| title_full_unstemmed | Exact formulas for the moments of the first passage time of reward processes |
| title_short | Exact formulas for the moments of the first passage time of reward processes |
| title_sort | exact formulas for the moments of the first passage time of reward processes |
| topic | semi-Markov process reward process Laplace transform first passage time |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/17 |
| work_keys_str_mv | AT gaparham exactformulasforthemomentsofthefirstpassagetimeofrewardprocesses |