The construction theory of denumerable Markov processes
著者
書誌事項
The construction theory of denumerable Markov processes
（Wiley series in probability and mathematical statistics, . Probability and mathematical statistics）
Hunan Science and Technology Pub. House , J. Wiley, c1990
- タイトル別名
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Kʿo lieh Ma-erh-kʿo-fu kuo chʿeng kou tsao lun
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注記
Translation of: Kʿo lieh Ma-erh-kʿo-fu kuo chʿeng kou tsao lun
Bibliography: p. 388-391
Includes index
内容説明・目次
内容説明
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.
目次
- Part 1: theoretical background
- introduction to construction theory
- construction of Q processes in simple cases
- uniqueness. Part 2 Construction theory of birth-death processes: bilateral birth-death processes
- birth-death processes. Part 3 Martin boundary and its application in the construction theory: Martin boundary and Q processes
- construction of Q processes with finite non-conservative states and finite exit boundary. Part 4 Path structure of denumerable Markov processes: the W transformation and strong limit
- leaping interval and entrance decomposition
- extension of processes. Part 5 Construction theory of birth-death processes - probability method: probability structure of birth-death processes
- relation between two kinds of construction theories of birth-death processes. Part 6 Properties of Markov processes related to construction theory: properties of birth-death processes
- recurrence and ergodic properties.
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