Nonhomogeneous fractional Poisson processes

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes WH(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 WH(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 λ(t  ) strongly influences the existence of the highest finite moment of WH(j)(t) and the behaviour of the tail probability of WH(j)(t).