A Non-Markovian Approach to a Stochastic Rumor Dynamics with Cognitive Deliberation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915913821847552 |
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| author | Coletti, Cristian F. Luiz, Denis A. |
| author_facet | Coletti, Cristian F. Luiz, Denis A. |
| contents | We introduce a non-Markovian rumor model on a complete graph of $n$ vertices, integrating the classical interactional framework of Daley and Kendall (1964) with modern cognitive insights into misinformation. Unlike traditional Markovian models, our approach incorporates a deliberation delay -- a decision-making window where individuals evaluate information before committing to dissemination or refutation. We establish a Functional Law of Large Numbers (FLLN) and a Functional Central Limit Theorem (FCLT) to characterize the asymptotic behavior and diffusion-scaled fluctuations of the process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07170 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Non-Markovian Approach to a Stochastic Rumor Dynamics with Cognitive Deliberation Coletti, Cristian F. Luiz, Denis A. Probability 60G55 (Primary), 60F17 (Secundary) We introduce a non-Markovian rumor model on a complete graph of $n$ vertices, integrating the classical interactional framework of Daley and Kendall (1964) with modern cognitive insights into misinformation. Unlike traditional Markovian models, our approach incorporates a deliberation delay -- a decision-making window where individuals evaluate information before committing to dissemination or refutation. We establish a Functional Law of Large Numbers (FLLN) and a Functional Central Limit Theorem (FCLT) to characterize the asymptotic behavior and diffusion-scaled fluctuations of the process. |
| title | A Non-Markovian Approach to a Stochastic Rumor Dynamics with Cognitive Deliberation |
| topic | Probability 60G55 (Primary), 60F17 (Secundary) |
| url | https://arxiv.org/abs/2407.07170 |