Critical branching processes in a sparse random environment
We introduce a branching process in a sparse random environment as an intermediate model between a Galton–Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and prove Yaglom-type limit theorems, that is, limit theorems for the...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
VTeX
2023-08-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/doi/10.15559/23-VMSTA231 |
| _version_ | 1827794956858687488 |
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| author | Dariusz Buraczewski Congzao Dong Alexander Iksanov Alexander Marynych |
| author_facet | Dariusz Buraczewski Congzao Dong Alexander Iksanov Alexander Marynych |
| author_sort | Dariusz Buraczewski |
| collection | DOAJ |
| description | We introduce a branching process in a sparse random environment as an intermediate model between a Galton–Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and prove Yaglom-type limit theorems, that is, limit theorems for the size of population conditioned on the survival event. |
| first_indexed | 2024-03-11T18:41:16Z |
| format | Article |
| id | doaj.art-d76b2fcd49f94a4884d0e6857af45dd4 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-03-11T18:41:16Z |
| publishDate | 2023-08-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-d76b2fcd49f94a4884d0e6857af45dd42023-10-12T13:05:16ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542023-08-0110439741110.15559/23-VMSTA231Critical branching processes in a sparse random environmentDariusz Buraczewski0Congzao Dong1Alexander Iksanov2Alexander Marynych3University of Wroclaw, Mathematical Institute, 50-384 Wroclaw, PolandXidian University, School of Mathematics and Statistics, 710126 Xi’an, ChinaTaras Shevchenko National University of Kyiv, Faculty of Computer Science and Cybernetics, 01601 Kyiv, UkraineTaras Shevchenko National University of Kyiv, Faculty of Computer Science and Cybernetics, 01601 Kyiv, UkraineWe introduce a branching process in a sparse random environment as an intermediate model between a Galton–Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and prove Yaglom-type limit theorems, that is, limit theorems for the size of population conditioned on the survival event.https://www.vmsta.org/doi/10.15559/23-VMSTA231Branching processfunctional limit theoremrandom environmentsurvival probability |
| spellingShingle | Dariusz Buraczewski Congzao Dong Alexander Iksanov Alexander Marynych Critical branching processes in a sparse random environment Modern Stochastics: Theory and Applications Branching process functional limit theorem random environment survival probability |
| title | Critical branching processes in a sparse random environment |
| title_full | Critical branching processes in a sparse random environment |
| title_fullStr | Critical branching processes in a sparse random environment |
| title_full_unstemmed | Critical branching processes in a sparse random environment |
| title_short | Critical branching processes in a sparse random environment |
| title_sort | critical branching processes in a sparse random environment |
| topic | Branching process functional limit theorem random environment survival probability |
| url | https://www.vmsta.org/doi/10.15559/23-VMSTA231 |
| work_keys_str_mv | AT dariuszburaczewski criticalbranchingprocessesinasparserandomenvironment AT congzaodong criticalbranchingprocessesinasparserandomenvironment AT alexanderiksanov criticalbranchingprocessesinasparserandomenvironment AT alexandermarynych criticalbranchingprocessesinasparserandomenvironment |