Fractional negative binomial and Pólya processes

Autor

  • Palaniappan Vellai Samy
  • Aditya Maheshwari

DOI:

https://doi.org/10.19195/0208-4147.38.1.5

Słowa kluczowe:

Fractional negative binomial process, fractional Pólya process, fractional Poisson process, infinite divisibility, Lévy process, PDEs

Abstrakt

In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Pólya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.

Pobrania

Opublikowane

2018-07-30

Numer

Dział

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