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