Probability and moment inequalities for additive functionals of geometrically ergodic Markov chains (Q6592137)

The authors derive concentration inequalities for linear statistics of Markov chains under a geometric Foster-Lyapunov drift condition and either aminorization condition or a local Wasserstein contraction. More specifically, the Bernstein- and Rosenthal-type inequalities for Markov chains are obtained using the cumulant techniques (see [\textit{V. P. Leonov} and \textit{A. N. Shiryaev}, Theory Probab. Appl. 4, 319--329 (1959; Zbl 0087.33701); translation from Teor. Veroyatn. Primen. 4, 342--355 (1959); \textit{L. Saulis} and \textit{V. Statulevičius}, Limit theorems for large deviations. Transl. from the Russian. Rev. and updated ed. Dordrecht etc.: Kluwer Academic Publishers (1991; Zbl 0744.60028)]) with explicit dependence on the initial distribution of the Markov chain and its mixing rate.