FSF3940 Probability
KTH Royal Institute of Technology
A Master’s degree in mathematics, applied mathematics or related field including at least 30 ECTS in mathematics. Recommended courses are SF2940 Probability theory and SF2743 Advanced real analysis I.
Probability is the mathematical theory for studying randomness and is one of the fundamental subjects in applied mathematics.For a rigorous treatment of probability, the measure theoretic approach is a vast improvement over the arguments usually presented in undergraduate courses. This course gives an introduction to measure theoretic probability and covers topics such as the strong law of large numbers, the central limit theorem, conditional expectations, and martingales. It is expected, but not required, that students have had some exposure to measure theory prior to taking this course. Students will practice by studying applications and solving problems related to the theory.
After completing the course students are expected to
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explain the foundations of probability in the language of measure theory,
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state the strong law of large numbers and give an outline of its proof
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have a basic knowledge of other 0-1 laws in probability
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have a working knowledge of weak convergence, characteristic functions, and the central limit theorem,
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give examples and applications of the strong law of large numbers and the central limit theorem,
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explain the concepts of recurrence and transience of random walks,
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explain the content of the Radon-Nikodym theorem and give an outline of its proof,
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explain the concept of conditional expectation, its properties and applications
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give an introduction to discrete time martingales and the martingale convergence theorem
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give examples and applications of martingales
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be able to solve basic problems related to the theory
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