In this paper, we aim to introduce a quantum linear stochastic Volterra integral equation of convolution type with operator-valued kernels in a nuclear topological algebra. We first establish the existence and uniqueness of the solutions and give the explicit expression of the solutions. Then we prove the continuity, continuous dependence on free terms and other properties of the solution.
Discrete-time normal martingale, Volterra integral equation, operator, existence and uniqueness
CHEN, JINSHU and TANG, YULING
"Quantum integral equations of Volterra type in terms of discrete-time normal martingale,"
Turkish Journal of Mathematics: Vol. 43:
3, Article 1.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/1