We generate the fractional Poisson process by subordinating the standard
Poisson process to the inverse stable subordinator. Our analysis is based on
application of the Laplace transform with respect to both arguments of the
evolving probability densities.Comment: 20 pages. Some text may overlap with our E-prints: arXiv:1305.3074,
arXiv:1210.8414, arXiv:1104.404