Finite-dimensional discrete linear stochastic accelerated-time systems and their application to quadratic stochastic dynamical systems

The limiting behavior of the trajectories {x⁽ⁿ⁾} of linear discrete stochastic systems of the form (K, P^an+b)_nN, whereK is the standard simplex in ^N,P:^{N N} is a linear operator,PK K,a ft,b ,a+b>0, is described. An application to a class of quadratic stochastic dynamical systems is considered.Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 709–718, May, 1996.