A Non-Markovian Approach to a Stochastic Rumor Dynamics with Cognitive Deliberation

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.