Further Topics in Probability, Spring 2019
| Joseph Najnudel; Márton Balázs | ||
| Email: | joseph.najnudel@our_city.ac.countrycode; m.balazs@our_city.ac.countrycode | |
| Offices: | 4.09 Howard House; 3.7 Main Bld | |
| Drop in Sessions: | Wednesdays 11:30 - 12:30, 4.09 Howard House (Weeks 13-18); 3.7 Maths (Weeks 19-24) | |
| Q&A Session: | Tuesday 28th May, 9:00am, SM3. Please prepare with questions. |
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Below is a detailed schedule. Topics of future events are plans, and can change. Topics of past events serve as log.
Homeworks are/will also be posted here: just click those with a link below. The green version uses less paper to print. They are due at 12:00pm in the blue locker with "Further Topics in Probability" on it on the ground floor of the Main Maths Building.
Homework solutions will appear on Blackboard, please email us if you have problem accessing these.
I was thinking about going over the ingenious proof of the SLLN by N. Etemadi, but decided to stay with the classical way instead. You are welcome to check out his way of doing it!
Came across this illustration of Jensen's inequality: square-root of the average ≠ average of the square-root.
| Day | Topics | Homework due: |
|---|---|---|
| Mon 28 Jan | Review of the unit, basic discrete distributions | -- |
| Tue 29 Jan | Basic discrete distributions; convolution (discrete cases) | -- |
| Thu 31 Jan | Ex. class (Neg.Bin convolution, continuous r.v., Normal distribution) | -- |
| Mon 4 Feb | Convolution (Gaussian) | -- |
| Tue 5 Feb | Convolution (Cauchy) | -- |
| Thu 7 Feb | Convolution (Cauchy) | HW1 HW1 (sol. on Bb.) |
| Mon 11 Feb | Gamma, Chi square distributions | -- |
| Tue 12 Feb | Poisson process. Generating functions (properties) | -- |
| Thu 14 Feb | Ex. class (convolutions) | -- |
| Mon 18 Feb | Generating functions (random no. of summands) | -- |
| Tue 19 Feb | Generating functions (Galton-Watson process) | -- |
| Thu 21 Feb | Generating functions (Critical G-W process; random walk) | HW2 HW2 (sol. on Bb.) |
| Mon 25 Feb | Generating functions (random walk: level 1 hitting time) | -- |
| Tue 26 Feb | Generating functions (weak convergence) | -- |
| Thu 28 Feb | Ex. class (fun with generating functions) | -- |
| Mon 4 Mar | Weak convergence examples, Weak Law of Large Numbers | -- |
| Tue 5 Mar | Weak Law of Large Numbers, Stirling's formula | -- |
| Thu 7 Mar | Stirling's formula, DeMoivre Laplace CLT | HW3 HW3 (sol. on Bb.) |
| Mon 11 Mar | DeMoivre Laplace CLT, Measure Theory (basic notions, probability) | -- |
| Tue 12 Mar | Measure Theory | -- |
| Thu 14 Mar | Ex. class (Generating functions: RW probabilities) | -- |
| Mon 18 Mar | Measure Theory | -- |
| Tue 19 Mar | Probabilistic tools | -- |
| Thu 21 Mar | Probabilistic inequalities | HW4 HW4 (sol. on Bb.) |
| Mon 25 Mar | Probabilistic inequalities; Convergences | -- |
| Tue 26 Mar | Convergences; Strong Law of Large Numbers (Kolmogorov's ineq.) | -- |
| Thu 28 Mar | Ex. class (convergence modes) | -- |
| Mon 1 Apr | Kolmogorov-Khinchin; Toeplitz' lemma | -- |
| Tue 2 Apr | Kronecker; Kolmogorov's Thm, SLLN | -- |
| Thu 4 Apr | Characteristic Functions | HW5 HW5 (sol. on Bb.) |
| Easter vacation | ||
| Mon 29 Apr | Inversion formula | -- |
| Tue 30 Apr | Inversion formula | -- |
| Thu 2 May | Ex. class (Characteristic functions) | -- |
|
Tue 7 May
|
Weak Convergence (Prokhorov's Thm) | -- |
| Tue 7 May | Weak Convergence (Continuity Lemma) | -- |
| Thu 9 May | WLLN, CLT, comments | HW6 HW6 (sol. on Bb.) |
If you have any questions, please contact us (see on top). Click here to see Márton's schedule.
To Márton's teaching page