### 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