Book contents
- Frontmatter
- Contents
- 1 Introduction and Overview
- 2 Preface to the Planning Chapters
- 3 Deterministic Decision Processes
- 4 Markov Chains
- 5 Markov Decision Processes and Finite Horizon Dynamic Programming
- 6 Discounted Markov Decision Processes
- 7 Episodic Markov Decision Processes
- 8 Linear Programming Solutions
- 9 Preface to the Learning Chapters
- 10 Reinforcement Learning: Model Based
- 11 Reinforcement Learning: Model Free
- 12 Large State Spaces: Value Function Approximation
- 13 Large State Space: Policy Gradient Methods
- 14 Regret Minimization
- Appendix A Dynamic Programming
- Appendix B Ordinary Differential Equations
- Reference
- Index
4 - Markov Chains
Published online by Cambridge University Press: 31 July 2026
Book contents
- Frontmatter
- Contents
- 1 Introduction and Overview
- 2 Preface to the Planning Chapters
- 3 Deterministic Decision Processes
- 4 Markov Chains
- 5 Markov Decision Processes and Finite Horizon Dynamic Programming
- 6 Discounted Markov Decision Processes
- 7 Episodic Markov Decision Processes
- 8 Linear Programming Solutions
- 9 Preface to the Learning Chapters
- 10 Reinforcement Learning: Model Based
- 11 Reinforcement Learning: Model Free
- 12 Large State Spaces: Value Function Approximation
- 13 Large State Space: Policy Gradient Methods
- 14 Regret Minimization
- Appendix A Dynamic Programming
- Appendix B Ordinary Differential Equations
- Reference
- Index
Summary
This chapter provides essential background on Markov chains as the foundation for Markov decision processes. The theory of state classification is developed, introducing accessibility relations, communicating classes and irreducibility. States are classified as recurrent or transient. The concept of periodicity is introduced. Central results concern invariant distributions – probability distributions that remain unchanged under the chain’s dynamics. Conditions for the existence and uniqueness of stationary distributions are established.
Keywords
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- Reinforcement Learning Foundations , pp. 36 - 45Publisher: Cambridge University PressPrint publication year: 2026
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