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Periodic solutions of stochastic discrete-time systems. (English) Zbl 0644.93056
We discuss the problem of the existence of periodic solutions of discrete-time systems with independent and periodic random perturbations. The discrete-time version of a result of R. Z. Khas’minskij [Stability of differential equations under random parameters (Russian) (1969; Zbl 0214.159)] is given. We also give necessary and sufficient conditions for the existence of periodic and stationary solutions of some affine stochastic discrete-time systems.

93E03 Stochastic systems in control theory (general)
34C25 Periodic solutions to ordinary differential equations
39A12 Discrete version of topics in analysis
93C55 Discrete-time control/observation systems