Eick, Ernst Christopher: Branching within branching in random environment. 2020
Inhalt
- Introduction
- The model
- The Ulam-Harris tree
- Informal description of the model
- Formal definition of the model
- The cell population
- The multiplication of parasites in a generational random environment
- The branching within branching process in random environment
- The process of parasites and further notation
- The space of host-parasite trees
- The process started in a cell v1 and the process started in the n-th generation
- The process of infected cells
- Size-biasing I
- The number of parasites along the spine I
- A Markov chain and the extinction-explosion principle for the process of parasites
- An extinction-explosion principle and the normalised process of infected cells
- The number of cells with a given number of parasites
- The process of parasites
- The a.s. extinction of the process of parasites
- The process of parasites and two martingales
- Size-biasing II
- The number of parasites along the spine II
- Main results in the case ¶(Surv)>0
- Linear fractional parasite reproduction
- The complete binary cell tree
- The model and known results about perpetuities
- The process of parasites along the spine
- The process of infected cells and related quantities
- The process of parasites
- The random cell tree
- Appendix
- Branching processes in random environment
- Branching processes in random environment with immigration
- Definitions and results from probability theory
- A lemma for the proof of Theorem 4.1 (b)
- The linear fractional distribution
- Acronyms
- List of symbols
- Bibliography
- Leere Seite