- Lecturer: Jan Obloj
Course Term: Michaelmas
Course Lecture Information: 5 hours of lectures in week -1.
Course Overview:
This short course gives a brief review of measure-theoretic probability, to include random variables, independence and conditional expectation, modes of convergence of random variable sequences, discrete-time martingales, and change of measure.
Course Synopsis:
Frequentist approach to probability; finite probability spaces; measure-theoretic approach to probability (general probability spaces); random variables; expectation; multi-dimensional random variables; independence; conditional expectation; convergence of random variables; Law of Large Numbers; characteristic functions; Central Limit Theorem; filtrations and stopping times; essentials of stochastic processes; martingales in discrete time; change of measure.