On the hitting times of continuous-state branching processes with immigration
We study a two-dimensional joint distribution related to the first passage time below a level for a continuous-state branching process with immigration. We provide an explicit expression of its Laplace transform and obtain a necessary and sufficient criterion for transience or recurrence. We follow...
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| Published in | Stochastic processes and their applications Vol. 124; no. 12; pp. 4182 - 4201 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.12.2014
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0304-4149 1879-209X |
| DOI | 10.1016/j.spa.2014.07.019 |
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| Abstract | We study a two-dimensional joint distribution related to the first passage time below a level for a continuous-state branching process with immigration. We provide an explicit expression of its Laplace transform and obtain a necessary and sufficient criterion for transience or recurrence. We follow the approach of Shiga (1990), by finding some λ-invariant functions for the generator. |
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| AbstractList | We study a two-dimensional joint distribution related to the first passage time below a level for a continuous-state branching process with immigration. We provide an explicit expression of its Laplace transform and obtain a necessary and sufficient criterion for transience or recurrence. We follow the approach of Shiga (1990), by finding some λ-invariant functions for the generator. |
| Author | Foucart, Clément Ma, Chunhua Duhalde, Xan |
| Author_xml | – sequence: 1 givenname: Xan surname: Duhalde fullname: Duhalde, Xan email: xan.duhalde@upmc.fr organization: PRES Sorbonne Universités, UPMC Université Paris 06, LPMA (UMR 7599), Boîte courrier 188, 4 place Jussieu, 75252 Paris Cedex 05, France – sequence: 2 givenname: Clément surname: Foucart fullname: Foucart, Clément email: foucart@math.univ-paris13.fr organization: Université Paris 13, Laboratoire Analyse, Géométrie & Applications, UMR 7539 Institut Galilée, 99 avenue J.B. Clément, 93430 Villetaneuse, France – sequence: 3 givenname: Chunhua orcidid: 0000-0002-7588-6681 surname: Ma fullname: Ma, Chunhua email: mach@nankai.edu.cn organization: Nankai University, School of Mathematical Sciences and LPMC, Tianjin 300071, PR China |
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| Cites_doi | 10.1214/EJP.v12-402 10.1016/0304-4149(76)90011-9 10.1007/s10959-010-0301-z 10.1016/j.spa.2012.03.012 10.1090/S0002-9904-1967-11762-2 10.1214/12-AOP766 10.1214/10-AOP629 10.1007/s004400050006 10.1016/0304-4149(84)90312-0 10.1016/j.spa.2004.11.003 10.1080/17442509408833880 10.1090/S0002-9904-1972-12938-0 10.1007/s004400100155 10.1016/j.bulsci.2008.10.001 10.1007/BF01203163 |
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| Keywords | Entrance time Continuous-state branching processes 60J80 Immigration Polarity Scale function Transience and recurrence 60J25 60G17 |
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| SubjectTerms | Continuous-state branching processes Entrance time Immigration Mathematics Polarity Probability Scale function Transience and recurrence |
| Title | On the hitting times of continuous-state branching processes with immigration |
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