Conditional McKean-Vlasov Differential Equations with Common Poissonian Noise: Propagation of Chaos
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929456163061760 |
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| author | Hernández-Hernández, Daniel Ricalde-Guerrero, Joshué Helí |
| author_facet | Hernández-Hernández, Daniel Ricalde-Guerrero, Joshué Helí |
| contents | A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated studying first both systems individually. Letting the population size growing to infinite, the weak convergence of the solutions of such systems is proved; in other words, propagation of chaos of such systems is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11564 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conditional McKean-Vlasov Differential Equations with Common Poissonian Noise: Propagation of Chaos Hernández-Hernández, Daniel Ricalde-Guerrero, Joshué Helí Probability 35Q70, 60B10, 60K35, 65C35, 82C22 A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated studying first both systems individually. Letting the population size growing to infinite, the weak convergence of the solutions of such systems is proved; in other words, propagation of chaos of such systems is obtained. |
| title | Conditional McKean-Vlasov Differential Equations with Common Poissonian Noise: Propagation of Chaos |
| topic | Probability 35Q70, 60B10, 60K35, 65C35, 82C22 |
| url | https://arxiv.org/abs/2308.11564 |