Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914227029016576 |
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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 |
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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 |