Approximation, Based On The Random Wavelet Neural Network For A Class Of Stochastic Processes

In this paper, we first review the development of wavelet analysis, wavelet transformation, wavelet nueral networks which are recently proposed and their application. On this basis, we first proposed a new type of stochastic neural networks-stochastic wavelet neural networks in this paper. Their convergence ,topology construction and non-linear learning principles are researched. The main contributins of this paper are described as follow:First, topology construction of stochastic wavelet neural networks and their non-linear learning principles are obtained. Also, the approximation property of stochastic wavelet neural network which is applied to a kind of stochastic processes are studied, and convergence rate are derived. Finally, we demonstrate the networks have special advantages by simulations, stochastic wavelet neural networks can be considered as a generalisation of wavelet neural networks in essence.