In this article, we study the ergodic risk-sensitive control problem for controlled regime-switching diffusions. Under a blanket stability hypothesis, solve associated nonlinear eigenvalue weakly coupled systems and characterize optimal stationary Markov controls via suitable verification theorem. We also consider near-monotone case obtain existence of principal eigenfunction controls.

In this paper, we prove a mean ergodic theorem for nonexpansive mappings in Hadamard (nonpositive curvature metric) spaces, which extends the Baillon nonlinear theorem. The main result shows that sequence given by Karcher means of iterations mapping with nonempty fixed point set converges weakly to mapping. This also remains true 1-parameter continuous semigroup contractions.

Given a stochastic nonlinear system controlled over possibly noisy communication channel, the article studies largest class of channels for which there exist coding and control policies so that closed-loop is stochastically stable. The stability criterion considered asymptotic mean stationarity (AMS). In this article, we develop general method based on ergodic theory probability to derive funda...

this paper provides a review on major ergodic features of semi-independent hyper mv {algebra dynamical systems. theorems are presentedto make contribution to calculate the entropy. particularly, it is proved that thetotal entropy of those semi-independent hyper mv {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...