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ST5214 Advanced Probability Theory (Sem 1:2009/10)
Probability: Theory and Examples by Durrett, Duxbury Press (main text)
Convergence of Stochastic Processes by Pollard, Springer
An Introduction to Probability Theory and its Applications by Feller, Wiley
Probability and Measure by Billingsley, Wiley
50% Graded Homework Assignments
50% Final Exam
Exam format
Open book (with restrictions)
ST2131 or Departmental Approval
Course contents
Probability measures and their distribution functions. Random variable: properties of
mathematical expectation, independence, conditional probability and expectation.
Convergence concepts: various modes of convergence of sequence of random variables;
almost sure convergence, Borel-Cantelli Lemma, uniform integrability, convergence of
moments. Weak and strong law of large numbers. Convergence in distribution,
characteristic function: general properties, convolution, uniqueness and inversion,
Lindeberg conditions and central limit theorem. This module is targeted at students who
are interested in Statistics and are able to meet the pre-requisites.