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DOI: 10.23952/cot.2023.38
Received August 4, 2022; Accepted October 29, 2022; Published October 3, 2023
Abstract. The first author recently derived several approximation results by neural network operators. There, the activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions. The results we apply here are univariate on a compact interval, regular and fractional. The outcome is the quantitative approximation of Brownian motion over the two dimensional sphere. We derive several Jackson type inequalities estimating the degree of convergence of our neural network operators to a general expectation function of Brownian motion. We give a detailed list of approximation applications regarding the expectation of well known functions of Brownian motion. Smoothness of our functions is taken into account producing higher speeds of approximation.
How to Cite this Article:
G.A. Anastassiou, D. Kouloumpou, Brownian motion approximation by neural networks, Commun. Optim. Theory 2023 (2023) 38.