Abstract
In this paper, a mathematical model of white Gaussian processes distributed in a bounded spatial domain is established in the framework of generalized function theory.First, both the spatially distributed white Gaussian process and the spatially distributed Wiener process are defined by introducing the concept of generalized random fields. It is also shown that the derivative of spatially distributed Wiener process with respect to time is the spatially distributed white Gaussian process in the sense of distributions.Secondly, the regularized distributed Wiener process with respect to spatial variables whose sample function is sufficiently smooth in the spatial domain defined is mathematically established. It is also verified that the regularized distributed Wiener process defined here satisfies the conditions of abstract Wiener processes defined by Curtain and Falb.Finally, a mathematical model of system noise distributed in a bounded spatial domain is approximately represented by the abstract Wiener integral.
