Meyn S Markov Chains and Stochastic Stability 2ed 2009

Textbook in PDF format

Communication and Regeneration
Heuristics
Markov models
Transition probabilities
Irreducibility
Pseudo-atoms
Topology and continuity
The nonlinear state space model
Stability Structures
Transience and recurrence
Harris and topological recurrence
The existence of π
Drift and regularity
Invariance and tightness
Convergence
Ergodicity
f-Ergodicity and f-regularity
Geometric ergodicity
V -Uniform ergodicity
Sample paths and limit theorems
Positivity
Generalized classification criteria
Epilogue to the second edition
Appendices
Mud maps
Testing for stability
Glossary of model assumptions
Some mathematical background