Time-continuous branching walk models of unstable gene amplification

DOI10.1007/BF02460646zbMath0804.92011OpenAlexW4250129057WikidataQ52380253 ScholiaQ52380253MaRDI QIDQ1319898

Marek Kimmel, David N. Stivers

Publication date: 19 April 1994

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02460646

zbMATH Keywords

Laplace transformsmodified Bessel functionsasymptotic expansionsprobability generating functionscancer cellscytotoxic agentsdeamplificationexpected number of cellsloss of resistancereversible drug resistancetime- continuous branching random walkunstable gene amplification

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Applications of branching processes (60J85) Medical applications (general) (92C50) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• Some stochastic models for plasmid copy number
• The dynamics of gene amplification described as a multitype compartmental model and as a branching process
• Conditional limit theorems for a left-continuous random walk