  This is the second part in a series of papers concerned with principal
Lyapunov exponents and principal Floquet subspaces of positive random dynamical
systems in ordered Banach spaces. The current part focuses on applications of
general theory, developed in the authors' paper "Principal Lyapunov exponents
and principal Floquet spaces of positive random dynamical systems. I. General
theory," Trans. Amer. Math. Soc., in press, to positive random dynamical
systems on finite-dimensional ordered Banach spaces. It is shown under some
quite general assumptions that measurable linear skew-product semidynamical
systems generated by measurable families of positive matrices and by strongly
cooperative or type-K strongly monotone systems of linear ordinary differential
equations admit measurable families of generalized principal Floquet subspaces,
generalized principal Lyapunov exponents, and generalized exponential
separations.
