Abstract:
We consider a Markov chain on $\mathbb R^+$ with asymptotically zero drift and finite second moments of jumps. We assume that the chain has invariant distribution. The paper is devoted to the existence and nonexistence of moments of invariant distribution. Our analysis is based on the technique of test functions.
Keywords:stationary Markov chain, asymptotically zero drift, invariant distribution, heavy-tailed distribution, power moments, Weibull-type moments, test (Lyapunov) functions, equilibrium identity.