We present the first empirical derivation of a continuous-time stochastic model for real-world opinion dynamics. Using longitudinal social-media data to infer users opinion on a binary climate-change topic, we reconstruct the underlying drift and diffusion functions governing individual opinion updates. We show that the observed dynamics are well described by a Langevin-type stochastic differential equation, with persistent attractor basins and spatially sensitive drift and diffusion terms. The empirically inferred one-step transition probabilities closely reproduce the transition kernel generated from the D-MODD model we introduce. Our results provide the first direct evidence that online opinion dynamics on a polarized topic admit a Markovian description at the operator level, with empirically reconstructed transition kernels accurately reproduced by a data-driven Langevin model, bridging sociophysics, behavioral data, and complex-systems modeling.

翻译：我们提出了首个基于实证推导的连续时间随机模型，用于描述真实世界的观点动力学。通过利用纵向社交媒体数据推断用户对二元气候变化话题的观点，我们重构了支配个体观点更新的潜在漂移和扩散函数。研究表明，观察到的动态过程可由朗之万型随机微分方程很好地描述，其中包含持久吸引子盆地以及空间敏感的漂移与扩散项。实证推断的单步转移概率精确复现了由我们所引入的D-MODD模型生成的转移核。我们的结果首次直接证明：在极化话题的在线观点动力学中，算子层面的马尔可夫描述成立，且实证重构的转移核可由数据驱动的朗之万模型精确复现，从而架起了社会物理学、行为数据与复杂系统建模之间的桥梁。