Neural Network Approximation for Time Splitting Random Functions

George A. Anastassiou () and Dimitra Kouloumpou
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George A. Anastassiou: Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA
Dimitra Kouloumpou: Section of Mathematics, Hellenic Naval Academy, 18539 Piraeus, Greece

Mathematics, 2023, vol. 11, issue 9, 1-25

Abstract: In this article we present the multivariate approximation of time splitting random functions defined on a box or R N , N ∈ N , by neural network operators of quasi-interpolation type. We achieve these approximations by obtaining quantitative-type Jackson inequalities engaging the multivariate modulus of continuity of a related random function or its partial high-order derivatives. We use density functions to define our operators. These derive from the logistic and hyperbolic tangent sigmoid activation functions. Our convergences are both point-wise and uniform. The engaged feed-forward neural networks possess one hidden layer. We finish the article with a great variety of applications.

Keywords: logistic and hyperbolic sigmoid functions; time splitting random function; neural network approximation; quasi-interpolation operator; multivariate modulus of continuity; stochastic inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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