Advanced Mathematics vol.2-Markov Skeleton Processes and Their Applications

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

Contents
1. Markov Skeleton Processes
2. Piecewise Deterministic Markov Skeleton Processes
3. Piecewise Deterministic Markov Processes
4. GI/I/1 Queueing Systems
5. Some Result on Inventory and Reliability Theory
6. Ruin Probability in the Continuous-Time Compound Binomial Model
7. Appendix A Elementary Knowledge
8. Appendix B Jump Processes and Their Martingales
9. Appendix C Ergodicity of Markov Processes and Markov Chains
Bibliography
Index