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Course image MA946:Introduction to graduate probability theory
2024/25
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
Notes on Large Deviations
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
Notes on Large Deviations
Course image PGCE International August 2019
Centre for Teacher Education