Invariant Probabilities of Transition Functions

• ​Introduction.- 1.Transition Probabilities .- 2.Transition Functions .- 3.Vector Integrals and A.E. Convergence .- 4.Special Topics.- 5.The KBBY Ergodic Decomposition, Part I.- 6.The KBBY Ergodic Decomposition, Part II.- 7.Feller Transition Functions.- Appendices: A.Semiflows and Flows: Introduction.- B.Measures and Convolutions.- Bibliography.- Index.

"The book is written with a high precision regarding definitions, notation, symbols and proofs. ... The book may serve specialists as a comprehensive review of the topic. On the other hand, because it is so clearly written and almost self-contained, it can be recommended as a perfect primer for beginners. ... The monograph is written for readers searching for an updated guide to functional methods of Markov (discrete- or continuous-time) processes." (Wojciech Bartoszek, Mathematical Reviews, November, 2015) "The present book is designed to provide a useful and complete presentation of the ergodic decomposition for transition functions defined on locally compact separable metric spaces. ... The book is of great interest not only to research workers in the field of dynamical systems and the theory of Markov processes but also to scientists such as biologists, physicists, etc. who need relatively straightforward rigorous mathematical methods in their studies and research as well." (Chryssoula Ganatsiou, zbMATH, Vol. 1302, 2015)