Edited by author 10-09-2003 05:17 PM
I believe what they meant by "joint statistics between two instants is shift-invariant" is that the autocorrelation ("joint statistics") between y(t1) and y(t2) is shift-invariant, i.e. wide-sense stationary. in other words, R(t1,t2) = E[y(t1)y(t2)] = E[y(t2+s)y(t2)] = R(s) where s is the time difference.

My take on what the statement "y(t) is from a second-order stationary stochastic process" means that y(t) has a finite autocorrelation (2nd order), and the autocorrelation is dependent on the time difference and the mean is constant (stationary).

A thought regarding the advantage of using Finsler distance is that according to this paper it's gauranteed to be positive "for MIMO systems" while Martin distance is not. Isn't always positive measures a requirement for making the space we're working in a Banach space, and therefore a bunch of other theory applies?