Models induced from critical birth–death process with random initial conditions

Tchorbadjieff, Assen; Mayster, Penka

doi:10.1080/02664763.2020.1732309

Cited by 5 publications

(4 citation statements)

References 22 publications

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“…Finally, the function A(t, s) in the series expansion (19), (20) for geometric branching reproduction is of exactly twice greater intensity β = 2K than the p.g.f. of the critical birth-death process, see [13]. In this case the lifetime parameter K > 0 (called killing rate) controls the intensity of reproduction and the size of population X(t), t > 0.…”

Section: Discussionmentioning

confidence: 99%

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Factorial moments of the critical Markov branching process with geometric reproduction of particles

Tchorbadjieff¹,

Mayster²

2022

Modern Stochastics: Theory and Applications

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The factorial moments of any Markov branching process describe the behaviour of its probability generating function $F(t,s)$ in the neighbourhood of the point $s=1$. They are applied to solve the forward Kolmogorov equation for the critical Markov branching process with geometric reproduction of particles. The solution includes quickly convergent recurrent iterations of polynomials. The obtained results on factorial moments enable computation of statistical measures as shape and skewness. They are also applicable to the comparison between critical geometric branching and linear birth-death processes.

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Section: Discussionmentioning

confidence: 99%

“…Proceeding with the summation by the following diagonals, j ≥ 2, as it is shown in Appendix, leads us to a generalised solution for coefficients a n,n−j and series expansion (13). Not surprisingly, working with diagonal forms implies the inclusion of combinatorial recurrent relations.…”

Section: Summation By Diagonalsmentioning

confidence: 99%

Factorial moments of the critical Markov branching process with geometric reproduction of particles

Tchorbadjieff¹,

Mayster²

2022

Modern Stochastics: Theory and Applications

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“…Birth and death can be described by using statistical data or stochastic processes [21]. Here, we assume that birth and death are only related to the size of the urban population.…”

Section: Kinetic Modelmentioning

confidence: 99%

Investigations to the Dynamics of City‐Size Distribution Containing Birth and Death Factors

Xia,

Huang

2023

Mathematical Problems in Engineering

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A kinetic model, which involves emigration, immigration, birth, death, and fluctuation terms, is utilized to investigate the evolution of city-size distribution. The Boltzmann-type equation and the corresponding Fokker–Planck equation are obtained to analyze the urban size distribution. Three different population variable functions, containing both birth and death rates, are considered. For each population variable function, the closed form of its stationary solution is derived. It is found that the size of urban population distribution follows a power law. Numerical simulation illustrates the correctness of the results.

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“…In this way, when the transmission is successful, the number of infectious individuals locally is doubled ( [1,3,4]).…”

Section: Introductionmentioning

confidence: 99%

On regime changes of COVID-19 outbreak

Tchorbadjieff

Томов

Velev

et al. 2023

Journal of Applied Statistics

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Models induced from critical birth–death process with random initial conditions

Cited by 5 publications

References 22 publications

Factorial moments of the critical Markov branching process with geometric reproduction of particles

Factorial moments of the critical Markov branching process with geometric reproduction of particles

Investigations to the Dynamics of City‐Size Distribution Containing Birth and Death Factors

On regime changes of COVID-19 outbreak

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