Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators

TL;DR

This paper introduces stochastic interpolation neural network operators with random coefficients, demonstrating their effectiveness in approximating stochastic processes with theoretical guarantees and potential applications in COVID-19 prediction.

Contribution

The paper develops a new class of stochastic interpolation neural network operators (SINNOs) with proven approximation properties for stochastic processes.

Findings

Proved boundedness and approximation accuracy of SINNOs.

Provided quantitative error estimates based on process continuity.

Showed potential application in COVID-19 case prediction.

Abstract

In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation capabilities in the mean square sense, in probability, as well as path-wise within the space of second-order stochastic (random) processes \( L^2(\Omega, \mathcal{F},\mathbb{P}) \). Additionally, we provide quantitative error estimates using the modulus of continuity of the processes. These results highlight the effectiveness of SINNOs for approximating stochastic processes with potential applications in COVID-19 case prediction.