**Requirements/prerequisites:**

**Duration:** Michaelmas, Hilary and Trinity

**Number of lectures per week:**

**Assessment:**

**End-of-year Examination:**

**Description: **

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.

Jun 10, 1998