Survival of Near-Critical Branching Brownian Motion
Consider a system of particles performing branching Brownian motion with negative drift, and killed upon hitting zero. Initially there is one particle at x > 0. Kesten (Stoch. Process. Appl. 7:9-47, 1978) showed that the process survives with positive probability if and only if ε > 0....
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1797086408161099776 |
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| author | Berestycki, J Berestycki, N Schweinsberg, J |
| author_facet | Berestycki, J Berestycki, N Schweinsberg, J |
| author_sort | Berestycki, J |
| collection | OXFORD |
| description | Consider a system of particles performing branching Brownian motion with negative drift, and killed upon hitting zero. Initially there is one particle at x > 0. Kesten (Stoch. Process. Appl. 7:9-47, 1978) showed that the process survives with positive probability if and only if ε > 0. Here we are interested in the asymptotics as ε→0 of the survival probability Qμ(x). It is proved that if, then for all x∈ℝ, lim ε→0Qμ(L+x)=θ(x)∈(0,1) exists and is a traveling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when x |
| first_indexed | 2024-03-07T02:21:37Z |
| format | Journal article |
| id | oxford-uuid:a41cafe9-40cc-47c9-9f2c-f1a1bf92144c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:21:37Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:a41cafe9-40cc-47c9-9f2c-f1a1bf92144c2022-03-27T02:31:43ZSurvival of Near-Critical Branching Brownian MotionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a41cafe9-40cc-47c9-9f2c-f1a1bf92144cEnglishSymplectic Elements at Oxford2011Berestycki, JBerestycki, NSchweinsberg, JConsider a system of particles performing branching Brownian motion with negative drift, and killed upon hitting zero. Initially there is one particle at x > 0. Kesten (Stoch. Process. Appl. 7:9-47, 1978) showed that the process survives with positive probability if and only if ε > 0. Here we are interested in the asymptotics as ε→0 of the survival probability Qμ(x). It is proved that if, then for all x∈ℝ, lim ε→0Qμ(L+x)=θ(x)∈(0,1) exists and is a traveling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when x |
| spellingShingle | Berestycki, J Berestycki, N Schweinsberg, J Survival of Near-Critical Branching Brownian Motion |
| title | Survival of Near-Critical Branching Brownian Motion |
| title_full | Survival of Near-Critical Branching Brownian Motion |
| title_fullStr | Survival of Near-Critical Branching Brownian Motion |
| title_full_unstemmed | Survival of Near-Critical Branching Brownian Motion |
| title_short | Survival of Near-Critical Branching Brownian Motion |
| title_sort | survival of near critical branching brownian motion |
| work_keys_str_mv | AT berestyckij survivalofnearcriticalbranchingbrownianmotion AT berestyckin survivalofnearcriticalbranchingbrownianmotion AT schweinsbergj survivalofnearcriticalbranchingbrownianmotion |