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Saigo space–time fractional Poisson process via Adomian decomposition method

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  • Kataria, K.K.
  • Vellaisamy, P.

Abstract

We obtain the state probabilities of various fractional versions of the classical homogeneous Poisson process using an alternate and simpler method known as the Adomian decomposition method (ADM). Generally these state probabilities are obtained by evaluating probability generating function using Laplace transform. A generalization of the space–time fractional Poisson process involving the Caputo type Saigo differential operator is introduced and its state probabilities are obtained using ADM.

Suggested Citation

  • Kataria, K.K. & Vellaisamy, P., 2017. "Saigo space–time fractional Poisson process via Adomian decomposition method," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 69-80.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:69-80
    DOI: 10.1016/j.spl.2017.05.007
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    1. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
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    Cited by:

    1. K. K. Kataria & M. Khandakar, 2022. "Generalized Fractional Counting Process," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2784-2805, December.
    2. Kataria, K.K. & Khandakar, M., 2022. "Extended eigenvalue–eigenvector method," Statistics & Probability Letters, Elsevier, vol. 183(C).
    3. Wang, Jiao & Xu, Tian-Zhou & Wang, Gang-Wei, 2018. "Numerical algorithm for time-fractional Sawada-Kotera equation and Ito equation with Bernstein polynomials," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 1-11.
    4. K. K. Kataria & P. Vellaisamy, 2019. "On Distributions of Certain State-Dependent Fractional Point Processes," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1554-1580, September.

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