Robustness analysis of a Continuous-Time Markov Jump Process model for herd behaviour under stochastic shocks

Herd behaviour in socio-economic systems is characterised by asynchronous, stochastic decision-making that traditional models capture imperfectly. Discrete-time DTMCs impose fixed-tick synchrony and require binning, which distorts event timing and smears off-grid shocks; deterministic compartmental models average out intrinsic randomness and cannot represent event-driven updates to switching propensities. We formulate an event-driven Continuous-Time Markov Jump Process (CTMJP) that models decisions via competing hazards and Kolmogorov forward equations, and we inject stochastic shocks directly into the generator to represent time-varying propensities to switch state. The contribution is threefold: (i) a mathematically explicit CTMJP with noise-in-rates capturing asynchronous choice and shock timing; (ii) a robustness framework based on discrepancy and information-theoretic functionals (MSE, RMSE, MAE, KL, Hellinger, entropy) together with sensitivity diagnostics; and (iii) a principled comparison against DTMC and deterministic baselines. In simulation, the CTMJP yields more faithful stochastic fluctuations, faster shock adaptation, and more realistic redistribution patterns than grid-based or purely deterministic alternatives, supporting its use for behavioural research, financial modelling, and policy simulation where timing and randomness are first-order features.