A localized coupling approach to interacting continuous-state branching processes
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917382907232256 |
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| author | Chen, Shukai Li, Pei-Sen Wang, Jian |
| author_facet | Chen, Shukai Li, Pei-Sen Wang, Jian |
| contents | We introduce a class of continuous-state branching processes with immigration, predation and competition, which can be viewed as a combination of the classical Lotka-Volterra model and continuous-state branching processes with competition that were introduced by Berestycki, Fittipaldi, and Fontbona (Probab. Theory Relat. Fields, 2018). This model can be constructed as a unique strong solution to a class of two-dimensional stochastic differential equations with jumps. We establish sharp conditions for the uniform ergodicity in the total variation of this model. Our proof relies on a novel, localized Markovian coupling approach, which is of its own interest in the ergodicity theory of Markov processes with interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03030 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A localized coupling approach to interacting continuous-state branching processes Chen, Shukai Li, Pei-Sen Wang, Jian Probability We introduce a class of continuous-state branching processes with immigration, predation and competition, which can be viewed as a combination of the classical Lotka-Volterra model and continuous-state branching processes with competition that were introduced by Berestycki, Fittipaldi, and Fontbona (Probab. Theory Relat. Fields, 2018). This model can be constructed as a unique strong solution to a class of two-dimensional stochastic differential equations with jumps. We establish sharp conditions for the uniform ergodicity in the total variation of this model. Our proof relies on a novel, localized Markovian coupling approach, which is of its own interest in the ergodicity theory of Markov processes with interactions. |
| title | A localized coupling approach to interacting continuous-state branching processes |
| topic | Probability |
| url | https://arxiv.org/abs/2604.03030 |