Extended eigenvalue–eigenvector method

K.K. Kataria and M. Khandakar

Statistics & Probability Letters, 2022, vol. 183, issue C

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.

Keywords: Eigenvalue–eigenvector method; Time fractional Poisson process; Fractional birth process (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109361

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