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Probability theory I, fall 2015


Teacher: Dario Gasbarra 

Scope: 5 op

Type: Advanced studies




Analysis I-II; Linear algebra and matrix calculus; vector analysis. 
Useful courses ( which are not compulsory prerequisites): probability calculus, functional analysis; measure and integral.



Teaching schedule

Weeks 36-43, Tuesday12-14 and Thursday 10-12 in room B120.


 The course is passed by writing a final exam. Attendance at lectures and

exercise classes is not compulsory (but recommended). Active participation to the exercise class

will raise your grade.   The next  exam is  on thursday 7.4.2016  (yleistentti).

It is possible to take this exam several times without limitations, you are always welcome to improve your grades.


Course material: lecture notes,  English version (last updated on 26.11.2015), Finnish version

Old probability theory course web pages with solved exercises: kevät 2009 syksy 2009syksy 2012syksy 2013  kevät 2015

 Old exam papers

exam problems and solutions, 29.10.2015suomenkielinen versio.

exam problems and solutions, 4.11.2015suomenkielinen versio.

The exam program consists of the first 6 chapters of the English version of the lecture notes,

 up to the chapter 6 on stochastic convergence (included),


One of these books

J.Jacod- P.Protter: Probability Essentials.

D. Williams: Probability with Martingales.

L. Koralov, Y. Sinai: Theory of Probability and Random Processes, Springer 2007.

Also recommended

O. Kallenberg: Foundations of Modern Probability.

P Malliavin, H Airault, L Kay, G Letac: Integration and Probability

A.N. Shiryaev: Probability  Springer.

A.N. Shiryaev: Problems in Probability, Springer 2012


Did you forget to register? What to do?



Exercise classes

1.Wednesday 10-12 C129 Dario Gasbarra 

Course feedback

Course feedback can be given at any point during the course. Click here.

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