Shortening of chromosome ends, known as telomeres, is one of the supposed mechanisms of cellular aging and death. We provide a probabilistic analysis of the process of loss of telomere ends. Theâ€¦ (More)

A general multi-type branching process where new individuals immigrate according to some point process is considered. An intrinsic submartingale is defined and a convergence result for processesâ€¦ (More)

We present a Poisson approximation with applications to extreme value theory. Let X1; X2; : : : be i.i.d. and let M (1) n Â¿M (2) n Â¿ Â· Â· Â·Â¿M ( j) n be the j largest order statistics. Then theâ€¦ (More)

The x logx condition is a fundamental concept for supercritical Galtonâ€“Watson branching processes, being the necessary and sufficient condition for the process to grow as its mean. In a Galtonâ€“Watsonâ€¦ (More)

A general branching process model is developed to analyse familial dependence in longevity data. A general formula for the survival function of a randomly chosen sibling of an individual of aâ€¦ (More)

A general branching process model is suggested to describe cell cycle desynchronization. Cell cycle phase times are modeled as random variables and a formula for the expected fraction of cells in Sâ€¦ (More)

Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson process are derived. The formulas are given in terms of iterates ofâ€¦ (More)

A general branching process model is proposed to describe the shortening of telomeres in eukariotic chromosomes. The model is flexible and incorporates many special cases to be found in theâ€¦ (More)