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Extended eigenvalue–eigenvector method

Author

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  • Kataria, K.K.
  • Khandakar, M.

Abstract

In this paper, we show that the eigenvalue–eigenvector method (EEM) and its extension can be utilized to obtain the state probabilities of Poisson-type counting processes. An extension of the EEM, namely, the extended eigenvalue–eigenvector method (EEEM) is introduced which can be used to solve the linear system of fractional differential equations involving Caputo fractional derivative. As an illustration, we obtain the known state probabilities of the time fractional Poisson process and the fractional birth process using the EEEM.

Suggested Citation

  • Kataria, K.K. & Khandakar, M., 2022. "Extended eigenvalue–eigenvector method," Statistics & Probability Letters, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:stapro:v:183:y:2022:i:c:s0167715221003011
    DOI: 10.1016/j.spl.2021.109361
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    References listed on IDEAS

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    1. Marina Popolizio, 2019. "On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation," Mathematics, MDPI, vol. 7(12), pages 1-12, November.
    2. 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.
    3. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
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