We present a class of Markov processes with multidimensional finite state space on which the infinitesimal transition movement is a shifting of one unit from one coordinate to some other to its right. We show how to represent the Kolmogorov forward equations as a triangular system.

A general theory of summation of divergent series based on the HardyKolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some cohomological equations, all solutions to which are nonmeasurable. In particular, this realizes a construction of a nonmeasurable function as first conjectured by Ko...

The properties of ω-limit set and global asymptotic behavior are first obtained for asymptotically autonomous discrete dynamical processes on metric spaces.Then certain equivalence of the asymptotic behavior between an asymptotically periodic semiflows and its associated asymptotically autonomous discrete dynamical process is proved. As some applications, the global behavior of asymptotically p...