Lecturer: Professor J T Lewis
Date: 1996-97
Groups: J.S./S.S. Mathematics
Prerequisites:
Duration: Michaelmas, Hilary and Trinity
Lectures per week:
Assessment:
Examinations:
I. Discrete Probability Spaces:
Sample Space, Events, Probabilities, Combination of Events.
Conditional Probabilities, Stochastic Independence, Random Variables,
Expectations, Conditional Expectations.
Random Walk: Probabilities of Ruin, Mean Duration, Reflection
Principle, Arc Sine Law.
Martingales: Application to Random Walk.
Markov Chains: Ergodic Theorem, Strong Markov property.
II. General Probability Spaces:
Measure Spaces, Events, Random Variables, Independence, Integration,
Expectations, Conditional Expectations.
Martingales:
Black-Scholes Theorem, The Kalman-Bucy Filter.
Weak Convergence, Central Limit Theorem.