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Probability Theory II
PhD in Statistics, Bocconi University
A.Y. 2016-2017
Instructor: Antonio Lijoi
Course Description.
The course will cover some fundamental topics in Probability Theory, including conditional
expectations and probabilities, weak convergence, central limit theorems and infinitely divisible
distributions.
Course Syllabus
• Convergence of laws
• Characteristic functions, inversion formula, Lévy’s continuity theorem
• Central limit theorems: independent and identically distributed summands, the Lindeberg and
Lyapunov theorems
• Infinitely divisible distributions
• The k-dimensional central limit theorem
• Conditional expectation, regular conditional probabilities, conditional independence
Textbooks
P. Billingsley (1995). Probability and Measure. 3rd Ed. Wiley, New York.
R. Dudley (2002). Real Analysis and Probability. Cambridge University Press.
Exam
Written and oral exam
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