The Construction Theory of Denumerable Markov Processes

This treatise is a summary of the author's research results on the construction theory of denumerable Markov processes. It provides an introduction to the analytical basis of the construction theory, and to the basic concepts and conclusions of random processes and Markov chains. The denumerable Markov processes form a very active and theoretically fairly complete branch of knowledge of Markov processes, which is universally applicable in many fields of science and technology. The construction problem is a central one, and the author's researches are mainly concentrated on the construction of birth-death processes in the construction theory, and of the Q processes with finite boundaries, on the probability method in the construction theory, and on the relationship between the probability method and the analytical method. The author has used these two methods to construct all the birth-death processes, and has meticulously investigated their properties. He has also derived all Q processes under the more extensive conditions that the non-conservative state and exit boundary of Q are both finite.
His treatise is not just a collection of achievements, but an elaborate stating and compilation of his research results.