Stochastic time scales: Quadratic Lyapunov functions and probabilistic regions of stability

We present a version of Lyapunov theory for stochastically generated time scales. In the case of quadratic Lyapunov functions for the LTI case, our results improve the requirement that spec(A) ⊂ H
_min
. Our approach also allows us to consider a special class of LTV problems where the dependence on time is only through the graininess.