Martingale Theory - Martingaaliteoria (MATS254, 4 cr)
Autumn 2011 - Syksy 2011
The course will be given in English.
Information and registration in Korppi system:
https://korppi.jyu.fi/kotka/r.jsp?course=119175.
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Kurssi luennoidaan englanniksi, tenttiä voi suomeksi tai englanniksi.
Kurssisivu ja ilmoittautuminen Korpissa:
https://korppi.jyu.fi/kotka/r.jsp?course=119175.
Contents - Sisältö
Conditional expectation, discrete time martingales, stopping times,
Optimal stopping theorem, convergence theorems, applications.
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Ehdollinen odotusarvo, diskreettiaikaiset martingaalit, pysäytyshetket,
Doobin pysäytyslause, martingaalien suppenemislauseita, sovelluksia.
Times and places
Lectures: 24 hours, starting on 13th September, 2011
Tuesdays 10-12 in MaD302 and Wednesdays 10-12 in MaD380
Exercises: 12 hours, starting on 20th September, 2011
Wednesdays 8.30-10 in MaD380
Examination on 2nd November, second chance on 23rd November, 2011.
Exercises
Problems for Session 1.
Problems for Session 2.
Problems for Session 3.
Problems for Session 4.
Problems for Session 5.
Problems for Session 6.
Solutions for Session 6.
Literature
- S. Geiss: Stochastic processes in discrete time,
Lecture notes 62. Available from Kampus Data; ask Tuula
(tuula.blafield"at"jyu.fi).
- D. Williams:
Probability with Martingales , Cambridge.
- J. Jacod, P. Protter: Probability Essentials,
Springer.
- A.N. Shiryaev: Probability, Springer.
- C. Geiss, S. Geiss: An Introduction to Probability Theory,
Lecture
notes
60.