Archive for the ‘Probability Theory’ Category

PhD Mathematics

December 29, 2011

For anyone interested, here are a few links to academic articles I wrote during my PhD on probability theory.

I would say that one of the most pleasing parts of the work I completed for my thesis was that we managed to find the right mathematical way to describe a complex problem, which essentially made it much easier to express and solve problems which had previously used quite intensive techniques.

There articles show applications of the main ideas and contain lots of interesting work on martingales, measure changes, and some pretty ideas on filtrations too. Enjoy!


The power of notation in problem solving

December 13, 2011

It’s trivial when you think about it:

good mathematical notation is one way of making a problem easier to solve.

In my introduction to advanced probability theory I put emphasis on how probability theory has developed a clever and natural way to describe the processes we deal with. If you think about it some more, the design of the notation is an important part of slicing the subject into manageable blocks.


A fast-moving introduction to advanced probability theory

November 30, 2011

Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory.

I was taught undergraduate probability theory by one of the best. Williams’s book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formal theoretical framework that holds probability together (I highly recommend going through all the exercises at the back of the book).