Approximation of time separating stochastic processes by neural networks revisited

Abstract

Here we study the univariate quantitative approximation of time separating stochastic process over the whole real line by the normalized bell and squashing type neural network operators. Activation functions here are of compact support. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged stochastic function or its high order derivative. The approximations are pointwise and with respect to the Lp norm. The feed-forward neural networks are with one hidden layer. We finish with a great variety of special applications.