Double Lusin Condition and Convergence Theorems for the Backwards Itô-Henstock Integral

Abstract

In this paper, we formulate an equivalent definition of the backwards Itô-Henstock integral of an operator-valued stochastic process with respect to a Hilbert space-valued \(Q\)-Wiener process using double Lusin condition. Moreover, we establish some versions of convergence theorems for this integral.