A note on Kurzweil-Henstock's anticipating non-stochastic integral
Yu Xin Ng, Tin Lam Toh
Received March 7, 2024. Published online December 5, 2024.
Abstract: Motivated by the study of anticipating stochastic integrals using Kurzweil-Henstock approach, we use anticipating interval-point pairs (with the tag as the right-end point of the interval) in studying non-stochastic integral, which we call the Kurzweil-Henstock anticipating non-stochastic integral. We prove the integration-by-parts and integration-by-substitution results, the convergence theorems using our new setting. Using the convergence theorems, we show that the Kurzweil-Henstock's anticipating non-stochastic integral is equivalent to the Lebesgue integral.
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Affiliations: Yu Xin Ng, Tin Lam Toh (corresponding author), National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, e-mail: tinlam.toh@nie.edu.sg
