On Henstock-Kurzweil method to Stratonovich integral

Stratonovich-Henstock integral for the operator-valued stochastic process

“…In this section, we shall define the Stratonovich-Henstock integral of an operator-valued stochastic process and enumerate some of its standard properties. This type of integral was first used in [28] for the real-valued stochastic process with respect to a Brownian motion. Throughout this paper, the given closed interval [0, T ] is nondegenerate, i.e.…”

“…In this section, we present a version of Itô's formula for the Stratonovich-Henstock integral, which turns out to be "ideal" [28] in the sense that the "tail" term has been removed. As a consequence, we can give the relationship between the Itô-Henstock and Stratonovich-Henstock integrals for the operator-valued stochastic process.…”

“…In [28], the authors used the generalized Riemann approach to define the Stratonovich integral of a real-valued process with respect to a Brownian motion. This newly defined integral encompasses the classical Stratonovich integral and satisfies the ideal Itô's formula.…”