Stability index of linear random dynamical systems

Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of stable manifold zero solution. In particular, for $n$ dimensional case, solution globally asymptotically if and only this $n.$ Fixed $n,$ let $X$ be random variable that assigns to each system index, $p_k$ with $k=0,1,\ldots,n,$ denote probabilities $P(X=k)$. paper we obtain either exact values $p_k,$ their estimations combining Monte Carlo method least square approach uses some affine relations among $p_k,k=0,1,\ldots,n.$ The particular case $n$-order differential difference equations also studied in detail.