On the fluctuation of stochastically monotone Markov chains and some applications

Abstract

A Borel–Cantelli-type property in terms of one-step transition probabilities is given for events like {|Xn +1| > a + ε, |Xn|≦a}, a and ε being two positive numbers. Applications to normed sums of i.i.d. random variables with infinite mean and branching processes in varying environment with or without immigration are derived.