Markov processes play an important role in the study of probability theory. Homogeneous denumerable Markov processes are among the main topics in the theory and have a wide range of application in various fields of science and technology (for example, in physics, cybernetics, queuing theory and dynamical programming). This book is a detailed presentation and summary of the research results obtained by the authors in recent years. Most of the results are published for the first time. Two new methods are given: one is the minimal nonnegative solution, the second the limit transition method. With the help of these two methods, the authors solve many important problems in the framework of denumerable Markov processes. I Construction Theory of Sample Functions of Homogeneous Denumerable Markov Processes.- I The First Construction Theorem.- II The Second Construction Theorem.- II Theory of Minimal Nonnegative Solutions for Systems of Nonnegative Linear Equations.- III General Theory.- IV Calculation.- V Systems of 1-Bounded Equations.- III Homogeneous Denumerable Markov Chains.- VI General Theory.- VII Martin Exit Boundary Theory.- VIII Martin Entrance Boundary Theory.- IV Homogeneous Denumerable Markov Processes.- IX Minimal Q-Processes.- X Q-Processes of Order One.- XI Arbitrary Q-Processes.- V Construction Theory of Homogeneous Denumerable Markov Processes.- XII Criteria for the Uniqueness of Q-Processes.- XIII Construction of Q-Processes.- XIV Qualitative Theory.
