Abstract
Consider the partial sums
Spectral theory. Well-behaved solutions
A "multiplicative" mean ergodic theorem. For all complex
Edgeworth expansions. Rates are obtained for the convergence of the distribution function of the normalized partial sums
Large deviations. The partial sums are shown to satisfy a large deviations principle in a neighborhood of the mean. This result, proved under geometric ergodicity alone, cannot in general be extended to the whole real line.
Exact large deviations asymptotics. Rates of convergence are obtained for the large deviations estimates above. The polynomial preexponent is of order
Extensions of these results to continuous-time Markov processes are also given.
Citation
I. Kontoyiannis. S. P. Meyn. "Spectral theory and limit theorems for geometrically ergodic Markov processes." Ann. Appl. Probab. 13 (1) 304 - 362, January 2003. https://doi.org/10.1214/aoap/1042765670
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