MSF600 Advanced topics in probability Spring 23

This page contains the topics which will be covered in the course: Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM (but everything is on this page that you need).

Program

The schedule of the course is in TimeEdit.

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Plan of lectures and corresponding literature

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Examination Information  

Note this is a pass-fail course for all students.

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Since integration theory is a prerequisite, I thought I would put up my notes from that course here so people can look up some things should they be needed.

Integration Theory Notes

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Various notes will be placed here.

Background notes relevant to Topic 6

Notes relevant to Topic 6

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Notes taken from the lectures will be placed here.

Topic 1: Background, Language, Kolmogorov 0-1 Law

Topic 2: Weak Law of Large Numbers, Triangular Arrays

Topic 3: Strong Law of Large Numbers: Part 1

Topic 4: Strong Law of Large Numbers: Part 2

Topic 5: Law of the Iterated Logarithm

Topic 6: Vague convergence

Topic 7: Characteristic Functions

Topic 8: Brownian Motion

Topic 9: Kakutani's Theorem

Topic 10: Stable and infinitely divisible distributions

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Homework will be placed here.

 

First homework, due Jan. 26

2nd Homework: Due February 17

3rd (and last) homework (Do March 10)

 

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