Linear-fractional Galton-Watson processes
Branching processes is an important part of modern Probability Theory.
Several monographs (two of them authored and one edited by our own Peter
Jagers) and many thousands of papers have been devoted to the theory and
applications of branching processes.
This course, worth 3 old credit points or 4.5 new points, deals with a
special class of branching processes with discrete time, so called
linear-fractional Galton-Watson processes. This class of branching
processes, although very narrow, allows for direct and rather elementary
calculations leading to beautiful asymptotic results with very
far-reaching generalizations.
The course will be comfortable to take for all PhD students at our
Mathematical Department even for those outside Mathematical Statistics
division. It would also be available for motivated Master degree
students.
Lecture notes
- can be downloaded from here
Timetable
- Lecture 1:
"Galton-Watson processes and probability generating functions"
slides 1-20, 114-117
Thursday, September 25, at 10.00-11.45, room MVL15
- Lecture 2: "Duality between the subcritical and supercritical cases"
(slides 21-33)
Tuesday, September 30, at 10.00-11.45, room MVL15
- Lecture 3: "Global limit theorems in the LF case"
(slides 34-42)
Thursday, October 2, at 10.00-11.45, room MVL15
- Lecture 4: "Multitype linear-fractional GWP"
(slides 94-104)
Tuesday, October 7, at 10.00-11.45, room MVL15
- Lecture 5: "Contour processes"
(slides 65-89, 105-110)
Thursday, October 9, at 10.00-11.45, room MVL15
- Lecture 6: "Size-biased linear-fractional GWP"
(slides 54-57, 62-64)
Tuesday, October 14, at 10.00-11.45, room MVL15
Participants
- Ottmar Cronie (1,2,3,4,6)
- Emilio Bergroth (4)
- Cristina Gutiérrez Pérez (1,2,3,4)
- Marcus Warfheimer (1)
- Stefan Eriksson (1,2,3,4,5,6)
- Peter Jagers (4)
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