This text provides a comprehensive presentation of results for time-homogeneous Markov chains with asymptotically zero drift. Including novel results and original research, this monograph will interest researchers and graduate students in probability, statistics and their applications.
Inhaltsverzeichnis
1. Introduction; 2. Lyapunov functions and classification of Markov chains; 3. Down-crossing probabilities for transient Markov chain; 4. Limit theorems for transient and null-recurrent Markov chains with drift proportional to 1/x; 5. Limit theorems for transient Markov chains with drift decreasing slower than 1/x; 6. Asymptotics for renewal measure for transient Markov chain via martingale approach; 7. Doob's h-transform: transition from recurrent to transient chain and vice versa; 8. Tail analysis for recurrent Markov chains with drift proportional to 1/x; 9. Tail analysis for positive recurrent Markov chains with drift going to zero slower than 1/x; 10. Markov chains with asymptotically non-zero drift in Cramé r's case; 11. Applications.
