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目录 15 Chapter 1 Markov Skeleton Processes 18 1.1 Concept of Markov Skeleton Processes 18 1.2 Backward and Forward Equations 21 1.3 Regularity Criteria 28 1.4 Finite Dimension Distribution 30 1.5 Limit Distribution 34 1.6 Generalized Limit Distribution and Invariant Probability Measure 43 1.7 Supplements and Notes 47 Chapter 2 Pieeewise Deterministic Markov Skeleton Processes 48 2.1 Definitions and Properties 48 2.2 Backward and Forward Equations and Regularity 52 2.3 Distribution and Moment of First Arrival Time 54 2.4 Necessary and Sufficient Condition to Be a Markov Process 59 2.5 Markov Modelling and Supplementary Variables 66 2.6 Supplements and Notes 69 Chapter 3 Piecewise Deterministic Markov Processes 70 3.1 Fundamental Definitions and Properties 70 3.1.1 Semi-dynamic system 70 3.1.2 The ø-memoryless distribution (family) 72 3.1.3 Stieltjes versions of exponentials and logarithms 76 3.1.4 The time-shift ø-invariant family A-functions 80 3.1.5 Time shift ø-invariant transition kernel 83 3.2 Extended Generator with Discrete Part 84 3.2.1 Standard piecewise deterministic Markov process 84 3.2.2 Extended generator with discrete part 85 3.2.3 The proof o

Author

ZHENTING HOU AND GUOXIN LIU

Publisher

International Press ; Science Press

Published

2005

Language

ZH

ISBN

9787030163417