  This paper deals with the study of principal Lyapunov exponents, principal
Floquet subspaces, and exponential separation for positive random linear
dynamical systems in ordered Banach spaces. The main contribution lies in the
introduction of a new type of exponential separation, called of type II,
important for its application to nonautonomous random differential equations
with delay. Under weakened assumptions, the existence of an exponential
separation of type II in an abstract general setting is shown, and an
illustration of its application to dynamical systems generated by scalar linear
random delay differential equations with finite delay is given.
