Well-posedness of a coupled system of Skorohod-like stochastic differential equations

Abstract

We study the well-posedness of a coupled system of Skorohod-like stochastic differential equations with reflecting boundary condition. The setting describes the evacuation dynamics of a mixed crowd composed of both active and passive pedestrians moving through a domain with obstacles, fire and smoke. As main working techniques, we use compactness methods and the Skorohod's representation of solutions to SDEs posed in bounded domains. This functional setting is a new point of view in the field of modeling and simulation pedestrian dynamics. The main challenge is to handle the coupling in the model equations together with the multiple-connectedness of the domain and the pedestrian-obstacle interaction.