On cross-correlogram IRF’s estimators of two-output systems in spaces of continuous functions

Abstract

In this article, single input–double output linear time-invariant systems are studied. Both components of system’s impulse response function are supposed to be real-valued and L 2-integrable. One component is unknown while the second one is controlled. The problem is to estimate the unknown component after observations of the other component. For this purpose, we apply cross-correlating of the outputs given that the input is a standard Wiener process on R. Weak asymptotic normality of appropriately centered estimators in spaces of continuous functions is proved. This enables us to construct confidence intervals in these spaces. Our results employ techniques related to Gaussian processes and bilinear forms of Gaussian processes.