Subexponential Concentration Inequalities for Bifurcating Markov Chains

In this paper, for bifurcating Markov chains, under weak and general conditions, we establish explicit subexponential concentration inequalities for different types of empirical means of unbounded functions. The subexponential concentration captures the tail behavior of distributions that are less concentrated than the Gaussian distribution. In particular cases, our results recover the existing subgaussian concentration.