a Department of Mathematical Sciences, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark
b Department of Management Science and Engineering, Stanford University, Stanford, CA 94305-4026, USA
Abstract:
A key result underlying the theory of MCMC is that any η-irreducible Markov chain having a transition density with respect to η and possessing a stationary distribution π is automatically positive Harris recurrent. This paper provides a short self-contained proof of this fact using the ergodic theorem in its standard form as the most advanced tool.