Age-Dependent Branching Processes with Non-homogeneous Poisson Immigration as Models of Cell Kinetics
- 44 Downloads
This article considers age-dependent branching processes with non-homogeneous Poisson immigration as models of cell proliferation kinetics. Asymptotic approximations for the expectation and variance–covariance functions of the process are developed. Estimators relying on the proposed asymptotic approximations are constructed, and their performance investigated using simulations.
KeywordsBellman–Harris branching process Renewal equation Quasi-likelihood Pseudo-likelihood Flow cytometry Leukemia Stem cells Oligodendrocytes
The paper is supported by NIH R01 grant AI129518 (Hyrien) and grant KP-6-H22/3 from the NSF of the Ministry of Education and Science of Bulgaria.
This research is supported by NIH grants AI129518, NS039511, CA134839, and AI069351 (Hyrien) and grant KP6-H22/3 from the NSF of the Ministry of Education and Science of Bulgaria. The authors are grateful to their colleagues Drs. Mark Noble, Margot Mayer-Pröschel, and Craig Jordan for valuable discussions about the biological examples that motivated this work.
- 22.Yakovlev, A. Y., Boucher, K., Mayer-Proschel, M., & Noble, M. (1998). Quantitative insight into proliferation and differentiation of oligodendrocyte-type 2 astrocyte progenitor cells in vitro. Proceedings of the National Academy of Sciences of the United States of America, 95, 14164–14167.Google Scholar
- 27.Yanev, N. M. (2008). Statistical inference for branching processes. In M. Ahsanullah & G. P. Yanev (Eds.), Records and branching processes (pp. 143–168). New York: NOVA Science Publishers.Google Scholar