Alexandru Lazari
Moldova State University, Vladimir Andrunachievici Institute of Mathematics and Computer Science, Chişinău, Moldova

Important properties of homogeneous linear recurrences over the set of complex numbers and its subsets are presented. We start with definition of generating vector and characteristic polynomial and formulate an efficient minimization method. Next, we go deeper into homogeneous linear recurrent processes over numerical rings and sign-based ring subsets. Littlewood, Newman and Borwein homogeneous linear recurrences are analyzed too. After that, the convergence, periodicity and boundedness of homogeneous linear recurrent processes are studied. Small perturbations in homogeneous linear recurrences are considered and asymptotic behavior is analyzed using Jury Stability Criterion. In the end, the stochastic systems with final sequence of states are defined and it is shown that their evolution time has a homogeneous linear recurrent distribution. The obtained results are applied for probabilistic characterization of the evolution time. Also, extended applications to games and optimization problems, defined on these stochastic systems, are mentioned.