Finite resolution of time in continuous measurements: phenomenology and the model

Definition of a quantum corridor describing monitoring a quantum observable in the framework of the phenomenological restricted-path-integral (RPI) approach is generalized for the case of a finite resolution of time. The resulting evolution of the continuously measured system cannot be presented by a differential equation. Monitoring of the position of a quantum particle is also considered with the help of a model which takes into account a finite resolution of time. The results based on the model are shown to coincide with those of the phenomenological approach.