Binary branching processes with Moran type interactions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866911835085602816 |
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| author | Cox, Alexander M. G. Horton, Emma Villemonais, Denis |
| author_facet | Cox, Alexander M. G. Horton, Emma Villemonais, Denis |
| contents | The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that may depend on the configuration of the whole system, the death of a particle may trigger the reproduction of another particle, while a branching event may trigger the death of an other one. We study the occupation measure of the new model, explicitly relating it to the Feynman-Kac semigroup of the underlying Markov evolution and quantifying the L2 distance between their normalisations. This model extends the fixed size Moran type interacting particle system discussed in [18, 19, 6, 7, 57] and we will indeed show that our model outperforms the latter when used to approximate a birth and death process. We discuss several other applications of our model including the neutron transport equation [36, 15] and population size dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03323 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Binary branching processes with Moran type interactions Cox, Alexander M. G. Horton, Emma Villemonais, Denis Probability The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that may depend on the configuration of the whole system, the death of a particle may trigger the reproduction of another particle, while a branching event may trigger the death of an other one. We study the occupation measure of the new model, explicitly relating it to the Feynman-Kac semigroup of the underlying Markov evolution and quantifying the L2 distance between their normalisations. This model extends the fixed size Moran type interacting particle system discussed in [18, 19, 6, 7, 57] and we will indeed show that our model outperforms the latter when used to approximate a birth and death process. We discuss several other applications of our model including the neutron transport equation [36, 15] and population size dynamics. |
| title | Binary branching processes with Moran type interactions |
| topic | Probability |
| url | https://arxiv.org/abs/2207.03323 |