Quantum integral equations of Volterra type in terms of discrete-time normal martingale

Abstract

In this paper, we aim to introduce a quantum linear stochastic Volterra integral equation of convolution typewith operator-valued kernels in a nuclear topological algebra. We first establish the existence and uniqueness of thesolutions and give the explicit expression of the solutions. Then we prove the continuity, continuous dependence on freeterms and other properties of the solution.