Teaching Methods. Classical teaching. Assignment of exercises, and correction by the teacher.
Verification of Learning. Written (2 hours, both theory and exercises) and oral exam.
More Information. If required, the course may be taught in English.
Objectives
The student will have to learn the basic notions of measure theory and probability theory. He will have to know the modern language of probability, and relate it to that of analysis. He will have to formalize and deal with problems arising in various areas of mathematics, developing the proofs. He will have to present some course topic. He will have to learn and study in an autonomous way.
Contents
Axioms of probability. Conditional probability and independence. Random variables. Construction of a probability measure. Integration. Characteristic functions. Convergence of random variables. The law of large numbers. The central limit theorem.
Texts
Jacod-Protter, Probability Essentials, Springer
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