Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators
This work addresses the approximation of stochastic processes, with potential applications in areas like COVID-19 case prediction, but appears incremental as it builds on existing neural network operator frameworks.
The paper tackles the problem of approximating random processes by constructing stochastic interpolation neural network operators (SINNOs) with random coefficients, establishing their boundedness, interpolation accuracy, and approximation capabilities in various senses, and providing quantitative error estimates using modulus of continuity.
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.