Stochastic Models of Cell Proliferation Kinetics Based on Branching Processes

Yanev, N. M.

doi:10.1007/978-3-030-34675-1_1

Statistical Modeling for Biological Systems 2020

DOI: 10.1007/978-3-030-34675-1_1

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Stochastic Models of Cell Proliferation Kinetics Based on Branching Processes

N. M. Yanev

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2024

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Diffusion approximation of critical controlled multi-type branching processes

Barczy,

González,

Martín-Chávez

et al. 2024

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion approximation is derived for some critical CMBPs. Namely, we consider a sequence of appropriately scaled random step functions formed from a critical CMBP with control distributions having expectations that satisfy a kind of linearity assumption. It is proved that such a sequence converges weakly toward a squared Bessel process supported by a ray determined by an eigenvector of a matrix related to the offspring mean matrix and the control distributions of the branching process in question. As applications, among others, we derive Feller-type diffusion approximations of critical, primitive multi-type branching processes with immigration and some two-sex branching processes. We also describe the asymptotic behaviour of the relative frequencies of distinct types of individuals for critical CMBPs.

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Diffusion approximation of critical controlled multi-type branching processes

Barczy,

González,

Martín-Chávez

et al. 2024

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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show abstract

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Stochastic Models of Cell Proliferation Kinetics Based on Branching Processes

Cited by 1 publication

References 18 publications

Diffusion approximation of critical controlled multi-type branching processes

Diffusion approximation of critical controlled multi-type branching processes

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