Studies on generalized Yule models

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 03 Dec 2018Embargo end date: 01 Jan 2018 Italy English Publisher:VTeXJournal:Modern Stochastics: Theory and Applications (issn: 2351-6046, eissn: 2351-6054,

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Authors: F. Polito;

doi: 10.15559/18-vmsta125 , 10.48550/arxiv.1803.07526

arXiv: 1803.07526

handle: 2318/1681532

Studies on generalized Yule models

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Abstract

We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes or a critical birth-death process. Further, in specific cases we derive the explicit form of the distribution of the number of species of a genus chosen uniformly at random for each time. Besides, we introduce a time-changed mixed Poisson process with the same marginal distribution as that of the time-fractional Poisson process.

Published at https://doi.org/10.15559/18-VMSTA125 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)

Country

Italy

Related Organizations

University of Turin
Italy

Keywords

T57-57.97, Applied mathematics. Quantitative methods, mixed Poisson processes, Yule model, mixed Poisson processes, time-fractional Poisson process, order statistics property, Probability (math.PR), Fractional processes, including fractional Brownian motion, Yule model, time-fractional Poisson process, Branching processes (Galton-Watson, birth-and-death, etc.), QA1-939, order statistics property, FOS: Mathematics, Point processes (e.g., Poisson, Cox, Hawkes processes), Yule model, Mixed Poisson processes, Time-fractional Poisson process, Order statistics property, Mathematics, Mathematics - Probability

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