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We study the well-posedness of a coupled system of Skorohod-like stochasticdifferential equations with reflecting boundary condition. The settingdescribes the evacuation dynamics of a mixed crowd composed of both active andpassive pedestrians moving through a domain with obstacles, fire and smoke. Asmain working techniques, we use compactness methods and the Skorohod'srepresentation of solutions to SDEs posed in bounded domains. This functionalsetting is a new point of view in the field of modeling and simulationpedestrian dynamics. The main challenge is to handle the coupling in the modelequations together with the multiple-connectedness of the domain and thepedestrian-obstacle interaction.

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