Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators

• URL: http://arxiv.org/abs/2512.24106v1
• Date: Tue, 30 Dec 2025 09:30:18 GMT
• Title: Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators
• Authors: Sachin Saini, Uaday Singh,
• Abstract summary: We construct a class of neural network operators (SINNOs) with random coefficients activated by sigmoidal functions.<n>We establish their boundedness, accuracy, and approximation capabilities in the mean sense, in probability, as well as path-wise within the space of second-order (random) processes.<n>Results highlight the effectiveness of SINNOs for approximating processes with potential applications in COVID-19 case prediction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \( L^2(Ω, \mathcal{F},\mathbb{P}) \). 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.

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