Central limit theorem for random processes with sample paths in exponential Orlicz spaces
The paper presents a central limit theorem for i.i.d. copies of a given process with sample paths in an exponential Orlicz space. The processes are indexed by a metric or pseudometric space \(T\). The main assumption of the theorem is that the exponential Orlicz norm (in the probability space) of the differences of the considered process is bounded by the distance of the indexes. The other assumption is some convenient integrability of the metric entropy of \(T\). The paper is completed by two examples: local time of Markov process and random Fourier series.
scientific article; zbMATH DE number 1134803