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Mixed-state branching evolution for cell division models

Part of: Markov processes Stochastic analysis

Published online by Cambridge University Press:  29 September 2025

Shukai Chen ,
Lina Ji Open the ORCID record for Lina Ji [Opens in a new window]  and
Jie Xiong
Shukai Chen*
Affiliation:
Fujian Normal University
Lina Ji*
Affiliation:
Shenzhen MSU-BIT University
Jie Xiong*
Affiliation:
Southern University of Science and Technology
*
*Postal address: School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007, China. Email: skchen@fjnu.edu.cn
**Postal address: MSU-BIT-SMBU Joint Research Center of Applied Mathematics, Shenzhen MSU-BIT University, Shenzhen 518172, China. Email: jiln@smbu.edu.cn
***Postal address: Department of Mathematics & National Center for Applied Mathematics (Shenzhen), Southern University of Science and Technology, Shenzhen 518055, China. Email: xiongj@sustech.edu.cn
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Abstract

We prove a scaling limit theorem for two-type Galton–Watson branching processes with interaction. The limit theorem gives rise to a class of mixed-state branching processes with interaction used to simulate evolution for cell division affected by parasites. Such processes can also be obtained by the pathwise-unique solution to a stochastic equation system. Moreover, we present sufficient conditions for extinction with probability 1 and the exponential ergodicity in the $L^1$-Wasserstein distance of such processes in some cases.

Keywords

Mixed-state branching processstochastic integral equationinteraction

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes 60H15: Stochastic partial differential equations

Information

Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 22
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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