A smooth 3D model for fiber lay-down processes

We present an improved three-dimensional stochastic model concerning the fiber lay-down in the production process of nonwoven materials. The model describes the position of the deposited fibers on a conveyor belt, which is determined by a system of stochastic differential equations. Here we remove a drawback of a previous 3D model, that is the non-smoothness of the fiber paths. Besides the derivation of the smooth 3D model we show its connection to the non-smooth model in a white noise limit.