Further Topics in Probability, Spring 2015
Márton Balázs  
Email:  m.balazs@our_city.ac.countrycode  
Tel:  +44 (0)117 9287991  
Office:  Maths 3.7  
Office hours:  Mondays 14:30  15:30 on teaching weeks, Maths 3.7  
except for the 16th of February, which is cancelled. 

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. They are due in class, or in the blue locker with my name on the ground floor of the Main Maths Building.
Homework solutions will appear on Blackboard, please email me 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: squareroot of the average ≠ average of the squareroot.
Day  Topics  Homework due: 

Mon 26 Jan, 13:00, Maths SM4  Review of the unit, basic discrete distributions   
Tue 27 Jan, 9:00, Maths SM4  Convolution (discrete cases)   
Tue 27 Jan, 14:00, Phys 3.34  Ex. Class (Neg.Binom and Uniform convolution; Residue Thm.)   
Thu 29 Jan, 15:00, Med C44  Convolution (Gaussian)   
Mon 2 Feb, 13:00, Maths SM4  Convolution (Cauchy)   
Tue 3 Feb 9:00, Maths SM4  Convolution (Cauchy, Exponential)   
Tue 3 Feb, 14:00, Phys 3.34  Ex. Class (Convolutions)  HW1 
Thu 5 Feb, 15:00, Med C44  Poisson process, Chi square; Generating functions (properties)   
Mon 9 Feb, 13:00, Maths SM4  Generating functions (examples; of convolutions)   
Tue 10 Feb, 9:00, Maths SM4  Generating functions (random no. of summands, GaltonWatson process)   
Tue 10 Feb, 14:00, Phys 3.34  Ex. Class (Generating functions)   
Thu 12 Feb, 15:00, Med C44  Generating functions (GaltonWatson process)   
Mon 16 Feb, 13:00, Maths SM4  Generating functions (random walk: level 1 hitting time)   
Tue 17 Feb, 9:00, Maths SM4  Generating functions (random walk, weak convergence)   
Tue 17 Feb, 14:00, Phys 3.34  Ex. Class (Generating functions)  HW2 
Thu 19 Feb, 15:00, Med C44  Generating functions (Poisson approximation)   
Mon 23 Feb, 13:00, Maths SM4  Weak Law of Large Numbers, Stirling's formula   
Tue 24 Feb, 9:00, Maths SM4  Normal distribution, DeMoivre Laplace CLT   
Tue 24 Feb, 14:00, Phys 3.34  Ex. Class (Generating fcts, WLLN, Stirling's formula)   
Thu 26 Feb, 15:00, Med C44  DeMoivre Laplace CLT   
Mon 2 Mar, 13:00, Maths SM4  Measure Theory (basic notions, probability)   
Tue 3 Mar, 9:00, Maths SM4  Measure Theory   
Tue 3 Mar, 14:00, Phys 3.34  Ex. Class (DeMoivre Laplace CLT), Weierstrass Approx. Thm.  HW3 
Thu 5 Mar, 15:00, Med C44  Probabilistic tools   
Mon 9 Mar, 13:00, Maths SM4  Probabilistic tools   
Tue 10 Mar, 9:00, Maths SM4  Notions of convergence   
Tue 10 Mar, 14:00, Phys 3.34  Ex. Class (Types of convergences)   
Thu 12 Mar, 15:00, Med C44  Convergences; Strong Law of Large Numbers (Kolmogorov's ineq.)   
Mon 16 Mar, 13:00, Maths SM4  Strong Law of Large Numbers (KolmogorovKhinchin, Toeplitz, Kronecker)   
Tue 17 Mar, 9:00, Maths SM4  Kolmogorov's Thm, SLLN   
Tue 17 Mar, 14:00, Phys 3.34  Ex. Class (Convergences, SLLN)  HW4 
Thu 19 Mar, 15:00, Med C44  Characteristic Functions   
Mon 23 Mar, 13:00, Maths SM4  Characteristic Functions (Inversion formula)   
Tue 24 Mar, 9:00, Maths SM4  Inversion formula, Weak Convergence   
Tue 24 Mar, 14:00, Phys 3.34  Ex. Class (Characteristic functions, Weak convergence)   
Thu 26 Mar, 15:00, Med C44  Weak Convergence, CLT (Prokhorov's Thm)   
Easter vacation  
Mon 20 Apr, 13:00, Maths SM4  Weak Convergence, CLT (Continuity Lemma)   
Tue 21 Apr, 9:00, Maths SM4  Weak Convergence, WLLN, CLT   
Tue 21 Apr, 14:00, Phys 3.34  Ex. Class (LLN, Characteristic functions, Lindeberg Thm)  HW5 
Thu 23 Apr, 15:00, Med C44  Weak Convergence, CLT (Comments on the CLT)   
Mon 27 Apr, 13:00, Maths SM4  Renewal Theory (LLN, Delayed renewals)   
Tue 28 Apr, 9:00, Maths SM4  Renewal Theory (Renewal theorems, stationary renewals)   
Tue 28 Apr, 14:00, Phys 3.34  Ex. Class (Age, renewal equation, renewal theorems)   
Thu 30 Apr, 15:00, Maths C44  Renewal Theory (residual time, proofs)   
Mon 4 May  Bank holiday  
Tue 5 May, 9:00, Maths SM4  Renewal Theory (Proofs)   
Tue 5 May, 14:00, Phys 3.34  Ex. Class (Gaps, terminating renewal)   
Thu 7 May, 15:00, Med C44  Renewal Theory (Proofs, renewal paradox, lengthbiased sampling)   
Fri 8 May, 16:00: HW6 deadline only  HW6  
Tue 12 May, 10:00, Maths SM3  Q&A session   
If you have any questions, please contact me (see on top). Below is my schedule.
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