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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.03265 |
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| _version_ | 1866914507056480256 |
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| author | Bayraktar, Erhan He, Xihao Kim, Donghan |
| author_facet | Bayraktar, Erhan He, Xihao Kim, Donghan |
| contents | We study a nonlinear graphon particle system driven by both idiosyncratic and common noise, where interactions are governed by a graphon and represented as positive finite measures. Each particle evolves via a McKean-Vlasov-type SDE with graphon-weighted conditional laws. We prove a law of large numbers for the empirical and interaction measures, using generalized Wasserstein metrics and weak convergence techniques suited for the non-Markovian structure induced by common noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graphon particle systems with common noise Bayraktar, Erhan He, Xihao Kim, Donghan Probability 05C80, 60K35, 28B20 We study a nonlinear graphon particle system driven by both idiosyncratic and common noise, where interactions are governed by a graphon and represented as positive finite measures. Each particle evolves via a McKean-Vlasov-type SDE with graphon-weighted conditional laws. We prove a law of large numbers for the empirical and interaction measures, using generalized Wasserstein metrics and weak convergence techniques suited for the non-Markovian structure induced by common noise. |
| title | Graphon particle systems with common noise |
| topic | Probability 05C80, 60K35, 28B20 |
| url | https://arxiv.org/abs/2507.03265 |