A note on asymptotic expansions for Markov chains using operator theory (Q1097570)

The author shows that the result of \textit{S. V. Nagaev} [Teor. Veroyatn. Primen 2, 389-416 (1958; Zbl 0078.318); English translation in Theory Probab. Appl. 2, 378-406 (1957)] on the decomposition of the characteristic function of a sum of random variables connected in a Markov chain can be proved under much weaker conditions. In particular he relaxes the conditional moment and ergodicity conditions (requiring exponentially fast convergence of the shift operator in \(L^ p\)-strong operator topology) to derive Nagaev's eigenvalue decomposition which might be used to derive expansion results for sums of Markov chain variables.