On a fractional linear birth-death process

DOI10.3150/10-BEJ263zbMath1284.60157arXiv1102.1620OpenAlexW1967279309MaRDI QIDQ637092

Federico Polito, Enzo Orsingher

Publication date: 2 September 2011

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.1620

zbMATH Keywords

fractional derivativesMittag-Leffler functionsfractional diffusion equationsextinction probabilitiesiterated Brownian motiongeneralized birth-death process

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (18)

Fractional linear birth-death stochastic process -- an application of Heun's differential equation ⋮ Non-local solvable birth-death processes ⋮ Asymptotic behavior and quasi-limiting distributions on time-fractional birth and death processes ⋮ Fractional diffusion-type equations with exponential and logarithmic differential operators ⋮ Fractional non-linear, linear and sublinear death processes ⋮ Queuing models with Mittag-Leffler inter-event times ⋮ Random-time processes governed by differential equations of fractional distributed order ⋮ The time evolution of the large exponential and power population growth and their relation to the discrete linear birth-death process ⋮ Modeling biological systems with an improved fractional Gompertz law ⋮ Asymptotic correlation structure of discounted incurred but not reported claims under fractional Poisson arrival process ⋮ Generalized fractional nonlinear birth processes ⋮ Transient behavior of fractional queues and related processes ⋮ Fractional immigration-death processes ⋮ On a jump-telegraph process driven by an alternating fractional Poisson process ⋮ On discrete-time semi-Markov processes ⋮ Probabilistic analysis of systems alternating for state-dependent dichotomous noise ⋮ On a fractional alternating Poisson process ⋮ On the sum of independent generalized Mittag–Leffler random variables and the related fractional processes

Cites Work

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• Fractional pure birth processes
• Fractional diffusion equations and processes with randomly varying time
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• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Fractional Poisson process
• Time-fractional telegraph equations and telegraph processes with Brownian time
• A fractional Poisson process in a model of dispersive charge transport in semiconductors
• FRACTIONAL PROCESSES: FROM POISSON TO BRANCHING ONE

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