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 $(K,P^{a^n+b})_{n\in\mathbb N}$, where $K$ is the standard simplex in ${\mathbb R}^N$, $P\colon{\mathbb R}^N\to{\mathbb R}^N$ is a linear operator, $PK\subset K$, $a\in\mathbb N$, $b\in\mathbb Z$, $a+b>0$, is described. An application to a class of quadratic stochastic dynamical systems is considered.