From multitype branching Brownian motions to branching Markov additive processes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908815246491648 |
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| author | Liang, Yutao Ren, Yan-Xia Shi, Quan Yang, Fan |
| author_facet | Liang, Yutao Ren, Yan-Xia Shi, Quan Yang, Fan |
| contents | We study a class of multitype branching Lévy processes, where particles move according to type-dependent Lévy processes, switch types via an irreducible Markov chain, and branch according to type-dependent laws. This framework generalizes multitype branching Brownian motions.
Using techniques of Markov additive processes, we develop a spine decomposition. This approach further enables us to prove convergence results for the additive martingales and derivative martingales, and establish the existence and uniqueness of travelling wave solutions to the corresponding multitype FKPP equations. In particular, applying our results to the on-off branching Brownian motion model resolves several open problems posed by Blath et al.(2025). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From multitype branching Brownian motions to branching Markov additive processes Liang, Yutao Ren, Yan-Xia Shi, Quan Yang, Fan Probability 60J80, 60G51, 35K57 We study a class of multitype branching Lévy processes, where particles move according to type-dependent Lévy processes, switch types via an irreducible Markov chain, and branch according to type-dependent laws. This framework generalizes multitype branching Brownian motions. Using techniques of Markov additive processes, we develop a spine decomposition. This approach further enables us to prove convergence results for the additive martingales and derivative martingales, and establish the existence and uniqueness of travelling wave solutions to the corresponding multitype FKPP equations. In particular, applying our results to the on-off branching Brownian motion model resolves several open problems posed by Blath et al.(2025). |
| title | From multitype branching Brownian motions to branching Markov additive processes |
| topic | Probability 60J80, 60G51, 35K57 |
| url | https://arxiv.org/abs/2512.21159 |