A Hierarchical Stochastic Differential Equation Framework with Particle-Filter Inference for Latent-State Dynamics around Life-Event Mentions on Reddit

We develop a hierarchical Ornstein–Uhlenbeck stochastic differential equation with event-conditional drift for latent-state dynamics around life events detected in text. Three formal results are established: existence and uniqueness of strong solutions; identifiability of the population-level parameters under sparse panel observation; and a posterior-bias bound for the drift estimator when event dates are known only to a coarser precision Δ than the observation grid. Inference combines a bootstrap particle filter with a Liu–West shrinkage kernel for the static hyperparameters, validated on synthetic data and against the exact Kalman posterior in the Gaussian special case. An empirical demonstration on approximately 1.7×10⁵ Reddit posts (2023-01 to 2024-12) estimates pre-event drift for four event types (n=696 users): none survives Benjamini–Hochberg correction, giving a calibrated null for the adequately powered job-change type and an underpowered non-detection for the other three.