Birth and Death Processes and Markov Chains
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内容提要：
This monograph offers a comprehensive survey of the area of birth death processes and Markov chains with continuous time parameters. For the English edition many new results have been added, bringing the book up-to-date and two new chapters were written specifically for this edition. .
This is the first systematic treatment of the subject in unified and compact book form. ... 编辑推荐：
This monograph offers a comprehensive survey of the area of birth death processes and Markov chains with continuous time parameters. For the English edition many new results have been added, bringing the book up-to-date and two new chapters were written specifically for this edition.
This is the first systematic treatment of the subject in unified and compact book form. 目录：
Preface. Chapter I General Concepts of Stochastic Processes §1.1 Definition of Stochastic Processes §1.2 Separability of Stochastic Processes §1.3 Measurability of Stochastic Processes §1.4 Conditional Probabilities and Conditional Mathematical Expectations §1.5 Markov Property §1.6 Transition Probabilities Chapter II Analytic Theory of Markov Chains §2.1 General Properties of Measurable Transition Matrices §2.2 Differentiability of Standard Transition Matrices §2.3 Backward and Forward Differential Equations §2.4 Standard Generalized Transition Matrices §2.5 Resolvent Matrices §2.6 The Minimal Q-Resolvent Matrices §2.7 Properties of the Minimal Q-Resolvent Matrix §2.8 Exit Families and Entrance Families §2.9 General Forms of Q-Resolvent Matrices §2.10 Construction of Q-Resolvent Matrices in Simple Cases 前言：
The objective of this book is to describe the fundamental theory of birthdeath processes and Markov chains and to present the developments in this field in recent years. The so-called Markov chain here refers to a Markov process which has continuous time parameters, countably many states and is time-homogeneous. Chains of this kind are important not only because its comparatively complete and unified theory can be used for reference in general Markov chains and other stochastic processes, but also because there is a steady increase in the ap..
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