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Stochastic Processes


Status Active - open for registrations
School IDA-gemensam (IDA)
Division STAT
Owner Krzysztof Bartoszek

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Course plan

No of lectures

Being planned out, ca 10lectures and some exercise sessions.

Recommended for

PhD students in a statistics related subject.

The course was last given

New course


On completion of the course, the students will be able to (see content
for specific theorems concepts covered):
1. Describes families of finite dimensional distributions using classical probability measures.
2. Evaluates characteristics of stochastic processes using probabilistic methods.
3. Finds analytical formulae for transition probabilities after elapsed time t.
4. Understand and assess asymptotic behavior of a stochastic process. Make statements about the asymptotic behaviour of a stochastic process.
5. Critically apply central results in probability theory for stochastic processes.


Background knowledge in probability theory, calculus, linear algebra.


Lectures and exercise sessions


1. Revision of selected parts of probability theory, in particular the moment generating function.
2. Stochastic processes - definition and examples.
3. Finite dimensional distributions of a stochastic process.
4. Homogeneous and non-homogeneou Poisson processes.
5. Markov chains, random walks, stochastic matrices.
6. Branching processes.
7. Martingales.
8. Doob Theorem.
9. Gaussian processes, Brownian motion.
10. Kolmogorov Theorem.


G. Grimmett, D., Stirzaker, Probability and Random Processes, Oxford University Press, 2020.
S. Ross, Stochastic Processes, John Wiley and Sons, 1996.



Course assessment consists of: oral presentation and/or written assignment dealing with goals 1,2,3,4,5 These elements must be passed to obtain a pass in the course.


Krzysztof Bartoszek




Course is currently being planned out.
Will be announced on Grapes once will be ready.

Page responsible: Director of Graduate Studies