We are concerned with a class of Cahn–Hilliard type stochastic interacting systems with stepping-stone noises. We first establish approximating SPDEs for them since the diffusion coefficients are not Lipschitz. And then we obtain the existence of weak mild solution to this system by solving a...

This note focuses on the Ornstein–Uhlenbeck process reflected at its long-run level (or long-run mean). The analytical closed-form of the transition density is obtained by virtue of the Skorokhod equation and the time-change for martingales. Our result is consistent with that presented by...

In this paper, we numerically investigate energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Boundary results in excess energy dissipation. The effects of the stochastic boundary conditions on energy dissipation are discussed. The...

In this paper, we numerically study energy dissipation per unit time per car Ed in the Nagel–Schreckenberg (NS) model. Numerical results show that there is a critical density over which energy dissipation occurs, but below which no energy loss happens in the deterministic NS model. Energy...