Approximation of Time Separating Stochastic Processes by Neural Networks

Abstract

Here we study the univariate quantitative approximation of time separating stochastic process over a compact interval or all the real line by quasi-interpolation neural network operators. We perform also the related fractional approximation. These approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged stochastic function or its high order derivative or fractional derivatives. Our operators are defined by using a density function induced by a general sigmoid function. The approximations are pointwise and with respect to the uniform norm. The feed-forward neural networks are with one hidden layer. We finish with a lot of interesting applications