Instructor: Balazs Rath

Prof. Balint Toth's lecture notes on limit theorems: CLICK

 

Prof. Balint Toth's lecture notes on large deviations (in Hungarian): CLICK

My hand-written, scanned lecture notes:

February 14 (large deviation thm for Binomial r.v.'s, relative entropy, crude Stirling formula): PDF (pages 0-7)

 

February 14 (exponential Chebyshev's inequality, logarithmic moment generating function, Legendre transform): PDF (pages 7-13)

 

February 25 (large dev. thm. for normal distribution, exponentially tilted distributions, convexity of log.mom.gen function): PDF (pages 14-19, in 2026, we skipped page the proof on 19 (Z is analytic) )

 

February 25 (convolution and tilting, Cramer's theorem, best strategy is to tilt optimally): PDF (pages 19-25)

 

March 4 (heuristics related to Cramer's thm, sum of GEO(p) large deviations, Hoeffding's inequality): PDF (pages 25-32), exercise sheet: PDF

 

March 4 (Bernstein's inequality, Fatou's lemma proof, dominated convergence theorem proof): PDF (pages 32-38, In 2026, we skipped page 33-35 (Bernstein's ineq) )

 

March 11 (c.d.f. properties, weak convergence, max of i.i.d. EXP(1), Gumbel, weak conv. of integer-valued r.v.'s): PDF (pages 39-45, In 2026, we skipped the proof of the claim stated on page 44 )

 

March 11 (BIN and POI, CLT for EXP(1), Stirling's formula, Scheffe's lemma, Slutsky's theorem): PDF (pages 46-52, In 2026, we skipped the proof on page 52 (Slutsky's proof) )

 

March 18 (local CLT for BIN(n,1/2) implies global CLT, random walk: reflection principle, limit thm for maximum and hitting time): PDF (pages 53-60)

 

March 18 (First midterm practice): Exercise sheet, Solutions