The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential
In this note we consider a branching Brownian motion (BBM) on R{double-struck} in which a particle at spatial position y splits into two at rate βy2, where β>0 is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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2010
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| _version_ | 1826286556910977024 |
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| author | Berestycki, J Brunet, É Harris, J Harris, S |
| author_facet | Berestycki, J Brunet, É Harris, J Harris, S |
| author_sort | Berestycki, J |
| collection | OXFORD |
| description | In this note we consider a branching Brownian motion (BBM) on R{double-struck} in which a particle at spatial position y splits into two at rate βy2, where β>0 is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while the population size remains finite, almost surely, for all time. We find an asymptotic for the almost-sure rate of growth of the population. © 2010 Elsevier B.V. |
| first_indexed | 2024-03-07T01:45:31Z |
| format | Journal article |
| id | oxford-uuid:9848b0f1-fcc4-4f49-84eb-9616960bb00e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:45:31Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:9848b0f1-fcc4-4f49-84eb-9616960bb00e2022-03-27T00:05:52ZThe almost-sure population growth rate in branching Brownian motion with a quadratic breeding potentialJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9848b0f1-fcc4-4f49-84eb-9616960bb00eEnglishSymplectic Elements at Oxford2010Berestycki, JBrunet, ÉHarris, JHarris, SIn this note we consider a branching Brownian motion (BBM) on R{double-struck} in which a particle at spatial position y splits into two at rate βy2, where β>0 is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while the population size remains finite, almost surely, for all time. We find an asymptotic for the almost-sure rate of growth of the population. © 2010 Elsevier B.V. |
| spellingShingle | Berestycki, J Brunet, É Harris, J Harris, S The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential |
| title | The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential |
| title_full | The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential |
| title_fullStr | The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential |
| title_full_unstemmed | The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential |
| title_short | The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential |
| title_sort | almost sure population growth rate in branching brownian motion with a quadratic breeding potential |
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