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Stochastic integrals of Itô and Henstock. (English) Zbl 0806.28009
The stochastic integral of Itô is defined measure theoretically, whereas the general theory of Henstock is defined using Riemann sums [see R. Henstock: “The general theory of integration” (1991; Zbl 0745.26006)]. The authors define the stochastic integral of Henstock and show that it includes that of Itô and that the corresponding Itô’s formula holds. However, it remains to give an example to show that there is a process which is integrable in the sense of Henstock but not of Itô.

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
60H05 Stochastic integrals