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Fundamental ideas in probability theory; sigma-fields, laws of large numbers, characteristic functions, the Central Limit Theorem, modes of convergence. Advanced topics may include Poisson random measures, random trees, Lévy processes, random spatial models. Students will undertake assigned individual research projects based on a journal article or advanced textbook, including a detailed explanation of the techniques of probability theory exemplified therein.

Fundamental ideas in probability theory; sigma-fields, laws of large numbers, characteristic functions, the Central Limit Theorem.

Fundamental ideas in probability theory; sigma-fields, laws of large numbers, characteristic functions, the Central Limit Theorem.

Fundamental ideas in probability theory; sigma-fields, laws of large numbers, characteristic functions, the Central Limit Theorem.

Fundamental ideas in probability theory; sigma-fields, laws of large numbers, characteristic functions, the Central Limit Theorem.