Topic: Recurrence and Transience

Recurrence and Transience in Finite Chains

Periodicity and the Timing of Returns

Path Enumeration for First Returns

Generating Functions for Return-Time Laws

First-Step Equations for Return Probabilities

First Passage Times in Discrete-Time Markov Chains

Explicit Examples of Transient States

Expected Visits and Return Probabilities

Every Finite Irreducible Chain Is Recurrent

Eventual Return Probability and Repeated Returns