Hegselmann--Krause model with environmental noise
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913582863613952 |
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| author | Chen, Li Nikolaev, Paul Prömel, David J. |
| author_facet | Chen, Li Nikolaev, Paul Prömel, David J. |
| contents | We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, the opinion of agents is modelled by an interacting particle system with a non-Lipschitz continuous interaction force, perturbed by idiosyncratic and environmental noises. Sending the number of agents to infinity, we derive a McKean-Vlasov stochastic differential equation as the limiting dynamic, by establishing propagation of chaos for regularized versions of the noisy opinion dynamics. To that end, we prove the existence of a unique strong solution to the McKean-Vlasov stochastic differential equation as well as well-posedness of the associated non-local, non-linear stochastic Fokker-Planck equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03955 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hegselmann--Krause model with environmental noise Chen, Li Nikolaev, Paul Prömel, David J. Probability Analysis of PDEs 60H15, 60H10, 60K35, 91D30 We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, the opinion of agents is modelled by an interacting particle system with a non-Lipschitz continuous interaction force, perturbed by idiosyncratic and environmental noises. Sending the number of agents to infinity, we derive a McKean-Vlasov stochastic differential equation as the limiting dynamic, by establishing propagation of chaos for regularized versions of the noisy opinion dynamics. To that end, we prove the existence of a unique strong solution to the McKean-Vlasov stochastic differential equation as well as well-posedness of the associated non-local, non-linear stochastic Fokker-Planck equation. |
| title | Hegselmann--Krause model with environmental noise |
| topic | Probability Analysis of PDEs 60H15, 60H10, 60K35, 91D30 |
| url | https://arxiv.org/abs/2301.03955 |