# MA946 - Introduction to Graduate Probability

**Lecturer: **Nikos Zygouras

**Term(s): **Term 1

**Commitment:** 30 lectures

**Assessment:** Oral exam (50%), Essay (50%)

**Prerequisites: **Familiarity with topics covered in ST111 Probability A & B; MA258 Mathematical Analysis III or MA259 Multivariate Calculus or ST208 Mathematical Methods or MA244 Analysis III; some MA359 Measure Theory or ST342 Maths of Random Events is useful.

**Material to be covered:**

- Reminder of measure theory
- modes of convergence
- law of large numbers
- central limit theorem (via characteristic functions, Lindeberg principle, Stein's method)
- stable laws
- large deviations
- martingales

**References:**

S.R.S. Varadhan, Probability Theory (Courant lecture notes), online notes

L. Breiman, Probability theory

F. den Hollander, Large Deviations

N. Zygouras, Discrete stochastic analysis