Chew, Tuan-Seng; Tay, Jing-Yi; Toh, Tin-Lam The non-uniform Riemann approach to Itô’s integral. (English) Zbl 1067.60025 Real Anal. Exch. 27(2001-2002), No. 2, 495-514 (2002). This paper proposes two approaches to the Itô’s integral in the line of generalized Riemann integrals of the Kurzweil-Henstock-McShane type. It is proved that the two approaches provide a stochastic integral which is equivalent to Itô’s one. The definitions are based upon McShane belated divisions, both with variable meshes in the line of the classical Kurzweil-Henstock-McShane integrals. The first definition, motivated by the Henstock lemma for classical integration, makes use of a suitable concept of additive function of meshed intervals. The second definition is a slight modification of a definition of the stochastic integral given by McShane. The basic properties of the integral are proved. Reviewer: Jean Mawhin (Louvain-La-Neuve) Cited in 1 ReviewCited in 12 Documents MSC: 60H05 Stochastic integrals 26A39 Denjoy and Perron integrals, other special integrals Keywords:Kurzweil-Henstock integral; Itô integral PDF BibTeX XML Cite \textit{T.-S. Chew} et al., Real Anal. Exch. 27, No. 2, 495--514 (2002; Zbl 1067.60025) Full Text: DOI OpenURL