Critical case stochastic phylogenetic tree model via the Laplace transform

• Autorzy: Bartoszek K. , Krzemiński M.
• Języki publikacji: EN

Abstrakty

EN

Birth–and–death models are now a common mathematical tool to describe branching patterns observed in real–world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth–and–death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non–trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this, we correct the proof of Liggett and Schinazi (2009) in the critical case.

Słowa kluczowe

EN

phylogenetic tree; stochastic model; Tauberian theory

PL

drzewo filogenetyczne; model stochastyczny; twierdzenie Taubera

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 2
• Strony: 474--481
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Bartoszek K.

• Mathematical Sciences, Chalmers University of Technology and The University of Gothenburg, 412 96 Göteborg, Sweden

autor

Krzemiński M.

• Department of Probability Theory and Biomathematics, Faculty of Applied Mathematics and Technical Physics, Gdansk University of Technology, 80-233 Gdansk, Poland
• Institute of Mathematics, Polish Academy of Sciences, 00-956 Warszawa, Poland

Bibliografia

• [1] P. Embrechts, E. Omey, Functions of power series, Yokohama Math. J. 32 (1984), 77–88.
• [2] L. C. Evans, Partial Differential Equations, AMS, 1998.
• [3] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley, New York, 1971.
• [4] J. Korevaar, Tauberian Theory: a Century of Developments, Springer, 2004.
• [5] T. M. Liggett, Total positivity and renewal theory, in Probablity, Statistics and Mathematics, Papers in Honor of Samuel Karlin, Academic Press, 1989.
• [6] T. M. Liggett, R. B. Schinazi, A stochastic model for phylogenetic trees, J. Appl. Probab. 46 (2009), 601–607.