Non-homogeneous Random Walks - Lyapunov Function Methods for Near-Critical Stochastic Systems

A modern presentation of the 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Aimed at researchers and research students in probability theory or a neighbouring field, the material will be accessible to anyone with some familiarity with the theory of Markov chains and discrete-time martingales.