Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators

Fuente: arXiv
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Main Authors: Saini, Sachin, Singh, Uaday
Format: Preprint
Published: 2025
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author Saini, Sachin
Singh, Uaday
author_facet Saini, Sachin
Singh, Uaday
contents 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 \( L^2(Ω, \mathcal{F},\mathbb{P}) \). 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_24106
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators
Saini, Sachin
Singh, Uaday
Machine Learning
Probability
41A05, 41A25, 41A28, 47A58, 60H35, 82C32
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 \( L^2(Ω, \mathcal{F},\mathbb{P}) \). 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.
title Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators
topic Machine Learning
Probability
41A05, 41A25, 41A28, 47A58, 60H35, 82C32
url https://arxiv.org/abs/2512.24106