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Poisson fractional processes. (English) Zbl 1042.60019
Summary: We propose a class of non-Gaussian stationary increment processes, named Poisson fractional processes \(W_H^{(j)}(t)\), which permit the study of the effects of long-range dependence in a large number of fields. The processes \(W_H^{(j)}(t)\) are self-similar in wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution.

MSC:
60G18 Self-similar stochastic processes
60G15 Gaussian processes
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