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Stochastic Processes2026VT, 7.5 credits
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Course plan
No of lectures
ca 10lectures and some exercise sessions.
Recommended for
PhD students in a statistics related subject.
The course was last given
2024VT
Goals
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.
Prerequisites
Background knowledge in probability theory, calculus, linear algebra.
Organization
Lectures and exercise sessions
Content
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.
Literature
G. Grimmett, D., Stirzaker, Probability and Random Processes, Oxford University
Press, 2020.
S. Ross, Stochastic Processes, John Wiley and Sons, 1996.
Lectures
Examination
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.
Examiner
Krzysztof Bartoszek
Credits
7.5hp
Comments
Will be announced on Grapes.
The course will also be open to outside of LiU students.
Page responsible: Anne Moe
