Schwach ergodische Prozesse

The term of the weak ergodic process respectable the weak ergodicty was defined for the first time by Landers and Rogge. It concerns the independence of each the random variables of a stationary process from the system of invariant sets of the same process. As it was already shown, the class of the weak ergodic processes is a genuine upper quantity of the class of all ergodic processes, which are the processes with a degenerated system of invariant sets. The basic request of the dissertation is the investigation, which characteristics, consequences and circumstances, e.g. the SLLN, whose validity was already proven for ergodic processes, remain true under the weaker conditions. Furthermore examples of weak ergodic processes are given and also the weak Ergodicity of Markov processes is examined. In addition a central limit theorem (CLT) for Martingal difference-sequences is indicated.



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