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

TL;DR

This paper presents a non-Markovian rumor model that incorporates cognitive deliberation delays, extending classical frameworks with modern insights, and provides rigorous asymptotic analysis of its behavior.

Contribution

It introduces a novel non-Markovian rumor model with deliberation delays and establishes its asymptotic laws, bridging classical and modern misinformation modeling.

Findings

Established a Functional Law of Large Numbers for the model.

Proved a Functional Central Limit Theorem describing fluctuations.

Characterized the asymptotic behavior of rumor spread with cognitive delays.

Abstract

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.