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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


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

Notes on Large Deviations

Additional material moodle page