Vladimir Vatutin: Vorlesung "Branching Processes and their Applications"

Vorlesung, 4 SWS
Termine:
Di, 14:00 - 16:00, 711 (groß)
Fr, 14:00 - 16:00, 711 (klein)
ab 12.4.2005

The course of lectures is devoted to branching processes and their applications in queueing theory and biology. It consists of two-level lectures. On Tuesdays we give a relatively non-formal description of the relevant results in branching processes (outlining mainly only the ideas of proofs) and describe possible applications of the formulated results while on Fridays we give technical details and formal proofs for more advanced mathmatical audience. We start by the classification of Markovian branching processes, describe relationships between branching processes and random walks, prove various limit theorems for such processes, investigate the distribution of the accumulated and maximal size of populations. Then we consider branching process bounded from above, study the distribution of the distance to the nearest common ancestor of the population, describe relationships between branching processes and a number of queueing systems such as SIRO (service in random order), systems with retrials, polling systems and some others. The second part of the course will be devoted to age-dependent (Bellman-Harris) branching processes, catalytic random walks, branching processes in random environment and applications of branching processes in study of the extinction risk of a population evolving in an autocorrelated environment.

 

Lecturenotes:
Lecture1.pdf
Lecture2.pdf
Lecture3.pdf
Lecture4.pdf
Lecture5.pdf
Lecture6.pdf
Lecture7.pdf
Lecture8.pdf
Lecture9.pdf
Lecture10.pdf
Lecture11.pdf
Lecture12.pdf
Lecture13.pdf
Lecture14.pdf
Lecture15.pdf



Letzte Änderung: 09.06.05/AWe