Contents

pp v-viii

1 - Introduction

pp 1-4

Part One - Consistencies

pp 5-6

2 - Strong Markov Consistency of Multivariate Markov Families and Processes

pp 7-37

3 - Consistency of Finite Multivariate Markov Chains

pp 38-48

4 - Consistency of Finite Multivariate Conditional Markov Chains

pp 49-66

5 - Consistency of Multivariate Special Semimartingales

pp 67-76

Part Two - Structures

pp 77-78

6 - Strong Markov Family Structures

pp 79-96

7 - Markov Chain Structures

pp 97-107

8 - Conditional Markov Chain Structures

pp 108-116

9 - Special Semimartingale Structures

pp 117-120

Part Three - Further Developments

pp 121-122

10 - Archimedean Survival Processes, Markov Consistency, ASP Structures

pp 123-127

11 - Generalized Multivariate Hawkes Processes

pp 128-178

Part Four - Applications of Stochastic Structures

pp 179-180

12 - Applications of Stochastic Structures

pp 181-194

Appendices

pp 195-258

Appendix A - Stochastic Analysis: Selected Concepts and Results Used in this Book

pp 197-208

Appendix B - Markov Processes and Markov Families

pp 209-217

Appendix C - Finite Markov Chains: Auxiliary Technical Framework

pp 218-221

Appendix D - Crash Course on Conditional Markov Chains and on Doubly Stochastic Markov Chains

pp 222-245

Appendix E - Evolution Systems and Semigroups of Linear Operators

pp 246-249

Appendix F - Martingale Problem: Some New Results Needed in this Book

pp 250-254

Appendix G - Function Spaces and Pseudo-Differential Operators

pp 255-258

References

pp 259-263

Notation Index

pp 264-265

Subject Index

pp 266-270