Markov Skeleton Processes and Their Applications实用数学手册（第2版）

Hhis book deals with the theory of Markov skeleton processes developed by authors and provides a systemeetic basis for the study of a variety of important stochastic processes including the GI/G/1process in queueing theory and piecewise deterministic Markov processes.Authors also use a lot of spplications of Markov sdeleton processes to queueing theory,inventory theory and risk theory.Most results in this book are published for the first time.
This book is sutiatle for graduate studients who have a basic grounding in probability theory and statistics,and also appeals to researchers who have interest in Markov processes and related fields.

Chapter 1 Markov Skeleton Processes
1.1 Concept to Markov Skeleton Processes
1.2 Backward and Forward Equations
1.3 Regularit Criteria
1.4 Finite Dimension Distribution
1.5 Limit Distribtion
1.6 Generalized Limit Distribution and Invariant Probability Measure
1.7 Supplements and Notes
Chapter 2 Piecewise Deterministic Markov Sheleton Process
2.1 Definitions and Properties
2.2 Backward and Forward Equations and Regulatity
2.3 Distribution and Moment of First Arrival Time
2.4 Necessary and Sufficient Condition to Be a Markov Process
2.5 Markov Modelling and Supplementary Variables
2.6 Supplements and Notes
Chapter 3 Piecewise Deterministic Markov Processes
3.1 Fudamental Definitions and Properties
3.2 Extended Generator with Discrete Part
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Chapter 4 GI/G/1Queueing Systems
Chapter 5 Some Result on Inventory and Reliability Theory
Chapter 5 Ruin Probability in the Continuous-Time Compound Binomial Model
Appendix A Elementary Knowledge
Appendix B Jump Processes and Their Martingales
Appendix C Ergodicity of Markov Processes and Markov Chains
Bibliography
Index

I first became aware of the work of Professor Hou because of his important contributions to the classical theory of Markov chains in late 1970's. This was one of the most important contributions to the theory of probability at that time and was very well appreciated by the international probability community. Among his many other contributions, the constructive theory of sample paths in Q-processes, the uniqueness criteria of Q-processes, and the work on totally instantaneous Q-processes by Professor Hou, have been considered as breakthrough..