Fractional linear birth-death stochastic process -- an application of Heun's differential equation

DOI10.1016/S0034-4877(18)30062-4zbMath1402.60109OpenAlexW2894824974WikidataQ115339902 ScholiaQ115339902MaRDI QIDQ1626331

Imre Pázsit, Hidetoshi Konno

Publication date: 27 November 2018

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(18)30062-4

zbMATH Keywords

generating functionmaster equationcritical fluctuationsfractional linear birth-death processwaiting time (lifetime) distribution

Mathematics Subject Classification ID

Applications of branching processes (60J85) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Continuous-time Markov processes on discrete state spaces (60J27) Fractional ordinary differential equations (34A08)

Cites Work

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• Fractional pure birth processes
• On a fractional linear birth-death process
• Some notes on the non-central negative binomial distribution
• Fractional Poisson process
• Factorization of the Heun's differential operator.
• Factorization of some confluent Heun's differential equations
• Exactly solvable birth and death processes
• Fractional kinetic equations: solutions and applications
• Species lifetime distribution for simple models of ecologies
• Orthogonal polynomials in Stein's method

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