School of Mathematics
Course 412 - Probability 1998-99 (J.S./S.S. Mathematics )
Lecturer: Professor J T Lewis


Duration: Michaelmas, Hilary and Trinity

Number of lectures per week:


End-of-year Examination:


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.


Black-Scholes Theorem, The Kalman-Bucy Filter.

Weak Convergence, Central Limit Theorem.

Jun 10, 1998

File translated from TEX by tth 1.46