Extinction times for a general birth, death and catastrophe process
The birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an...
| Auteurs principaux: | , |
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| Format: | Journal article |
| Langue: | English |
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2004
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| _version_ | 1826284016082354176 |
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| author | Cairns, B Pollett, P |
| author_facet | Cairns, B Pollett, P |
| author_sort | Cairns, B |
| collection | OXFORD |
| description | The birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction, and the distribution of the population size conditional on nonextinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We address this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times. © Applied Probability Trust 2004. |
| first_indexed | 2024-03-07T01:07:30Z |
| format | Journal article |
| id | oxford-uuid:8bda899f-bc27-4c30-b0eb-3cfe8a135ad8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:07:30Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:8bda899f-bc27-4c30-b0eb-3cfe8a135ad82022-03-26T22:40:48ZExtinction times for a general birth, death and catastrophe processJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8bda899f-bc27-4c30-b0eb-3cfe8a135ad8EnglishSymplectic Elements at Oxford2004Cairns, BPollett, PThe birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction, and the distribution of the population size conditional on nonextinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We address this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times. © Applied Probability Trust 2004. |
| spellingShingle | Cairns, B Pollett, P Extinction times for a general birth, death and catastrophe process |
| title | Extinction times for a general birth, death and catastrophe process |
| title_full | Extinction times for a general birth, death and catastrophe process |
| title_fullStr | Extinction times for a general birth, death and catastrophe process |
| title_full_unstemmed | Extinction times for a general birth, death and catastrophe process |
| title_short | Extinction times for a general birth, death and catastrophe process |
| title_sort | extinction times for a general birth death and catastrophe process |
| work_keys_str_mv | AT cairnsb extinctiontimesforageneralbirthdeathandcatastropheprocess AT pollettp extinctiontimesforageneralbirthdeathandcatastropheprocess |