Book contents
- Frontmatter
- Contents
- 1 Introduction
- Part One Consistencies
- 2 Strong Markov Consistency of Multivariate Markov Families and Processes
- 3 Consistency of Finite Multivariate Markov Chains
- 4 Consistency of Finite Multivariate Conditional Markov Chains
- 5 Consistency of Multivariate Special Semimartingales
- Part Two Structures
- Part Three Further Developments
- Part Four Applications of Stochastic Structures
- Appendices
- References
- Notation Index
- Subject Index
3 - Consistency of Finite Multivariate Markov Chains
from Part One - Consistencies
Published online by Cambridge University Press: 18 September 2020
- Frontmatter
- Contents
- 1 Introduction
- Part One Consistencies
- 2 Strong Markov Consistency of Multivariate Markov Families and Processes
- 3 Consistency of Finite Multivariate Markov Chains
- 4 Consistency of Finite Multivariate Conditional Markov Chains
- 5 Consistency of Multivariate Special Semimartingales
- Part Two Structures
- Part Three Further Developments
- Part Four Applications of Stochastic Structures
- Appendices
- References
- Notation Index
- Subject Index
Summary
In this chapter the concept of strong Markov consistency and the concept of weak Markov consistency for finite time-inhomogeneous multivariate Markov chainsis introduced and studied. In particular, necessary and sufficient conditions for both types of Markov consistency are given. The main tool used here is the semimartingale characterization of finite Markov chains. In addition, operator interpretation of a sufficient condition for strong Markov consistency and a necessary condition for weak Markov consistency are provided.By definition, strong Markov consistency implies the weak Markov consistency. In this chapter we provide sufficient condition for the reverse implication to hold.
- Type
- Chapter
- Information
- Structured Dependence between Stochastic Processes , pp. 38 - 48Publisher: Cambridge University PressPrint publication year: 2020