Online inference of lane changing events for connected and automated vehicle applications with analytical logistic diffusion stochastic differential equation

•The stochastic lane-changing trajectory is modeled with the logistic diffusion method, which is represented by a stochastic differential equation. The analytical solution is derived.•The analytical distribution of the lateral movement is solved by the Fokker Planck equation.•A procedure of inferring lane changing initiation moment (LCIM), cross-lane-mark moment (CLMM), and lane changing duration (LCD) is established.•The proposed method is tested against real-world data. The results are encouraging.