At the Edge of Criticality: Markov Chains with Asymptotically Zero Drift

Understand

The main goal of this text is comprehensive study of time homogeneous Markov chains on the real line whose drift tends to zero at infinity, we call such processes Markov chains with asymptotically zero drift.

• Traditionally this topic is referred to as Lamperti's problem.
• Time homogeneous Markov chains with asymptotically zero drift may be viewed as a subclass of perturbed in space random walks.
• The latter are of basic importance in the study of various applied stochastic models, among them branching and risk processes, queueing systems etc.