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Nonhomogeneous fractional Poisson processes. (English) Zbl 1137.60322
Summary: We propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes \(W_H^{(j)}(t)\), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes \(W_H^{(j)}(t)\) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function \(\lambda (t)\) strongly influences the existence of the highest finite moment of \(W_H^{(j)}(t)\) and the behaviour of the tail probability of \(W_H^{(j)}(t)\).

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