Fractional pure birth processes

DOI10.3150/09-BEJ235zbMath1284.60156arXiv1008.2145MaRDI QIDQ637084

Enzo Orsingher, Federico Polito

Publication date: 2 September 2011

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.2145

zbMATH Keywords

branching processesstable processesMittag-Leffler functionsAiry functionsYule-Furry processiterated Brownian motionnonlinear birth processDzherbashyan-Caputo fractional derivativeVandermonde determinants

Mathematics Subject Classification ID

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

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Cites Work

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• Fractional Poisson process. II
• Fractional diffusion equations and processes with randomly varying time
• Fractional Poisson processes and related planar random motions
• 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
• Poisson fractional processes
• Fractional master equation: Non-standard analysis and Liouville-Riemann derivative
• A note on alternating sums
• Nonhomogeneous fractional Poisson processes
• A fractional Poisson process in a model of dispersive charge transport in semiconductors
• FRACTIONAL PROCESSES: FROM POISSON TO BRANCHING ONE