Mixed state branching evolution for cell division models
Preprint
Abstract
We prove a scaling limit theorem for two-type Galton-Waston branching processes with interaction. The limit theorem gives rise to a class of mixed state branching processes with interaction using to simulate the evolution for cell division affected by parasites. Such process can also be obtained by the pathwise unique solution to a stochastic equation system. Moreover, we present sufficient conditions for extinction with probability one and the exponential ergodicity in the total variation distance of such process.Keywords
All Related Versions
This publication has 9 references indexed in Scilit:
- A scaling limit of controlled branching processesStatistics & Probability Letters, 2024
- Superprocesses for the Population of Rabbits on GrasslandProceedings of the Steklov Institute of Mathematics, 2022
- Continuous Time Mixed State Branching Processes and Stochastic EquationsActa Mathematica Scientia, 2021
- A general continuous-state nonlinear branching processThe Annals of Applied Probability, 2019
- Stochastic equations, flows and measure-valued processesThe Annals of Probability, 2012
- Stochastic equations of non-negative processes with jumpsStochastic Processes and their Applications, 2010
- A limit theorem of two-type Galton–Watson branching processes with immigrationStatistics & Probability Letters, 2009
- Skew convolution semigroups and affine Markov processesThe Annals of Probability, 2006
- Branching Processes with Immigration and Related Limit TheoremsTheory of Probability & Its Applications, 1971