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Zeitschrift für Analysis und ihre Anwendungen


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Volume 7, Issue 4, 1988, pp. 289–307
DOI: 10.4171/ZAA/307

Published online: 1988-08-31

General Limit Theorems with $o$-Rates and Markov Processes under Pseudo-Moment Conditions

Paul L. Butzer[1] and Heribert Kirschfink[2]

(1) Rheinisch-Westfälische Technische Hochschule Aachen, Germany
(2) Rheinisch-Westfälische Technische Hochschule Aachen, Germany

Making use of the Dvoretzky extension of the Trotter-operator method, a general convergence theorem with $o$-rates for dependent, real-valued random variables satisfying a pseudo-moment condition is established. Applications are to general convergence theorems, a central limit theorem as well as a weak law of large numbers for Markov processes with discrete time parameter. Further, pseudo-moment conditions are discussed in detail and the results are compared with the theory of probability-metrics.

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Butzer Paul , Kirschfink Heribert: General Limit Theorems with $o$-Rates and Markov Processes under Pseudo-Moment Conditions. Z. Anal. Anwend. 7 (1988), 289-307. doi: 10.4171/ZAA/307