Criteria for the non-ergodicity of stochastic processes: application to the exponential back-off protocol
Guy Fayolle, Rudolph Iasnogorodski · Journal of Applied Probability · 1987
In this paper, we present some simple new criteria for the non-ergodicity of a stochastic process (Yn), n ≧ 0 in discrete time, when either the upward or downward jumps are majorized by i.i.d. random variables. This situation is encountered in many practical situations, where the (Yn) are functionals of some Markov chain with countable state space. An application to the exponential back-off protocol is described.