Lecture notes
- Week 1, Discrete time Gaussian processes
- Week 2, Discrete state space Markov chains
- Week 3, Continuous time Gaussian processes
- Week 4, Brownian motion and the heat equation
- Week 5, The Ito integral, part 1
- Week 6, Ito's lemma
- Week 7, Introduction to general diffusions
- Week 8, Hitting times and martingales (to be completed)
- Week 9, Stochastic differential equations and their solution
- Week 10, Change of measure and Girsanov's formula
- Week 11, Feynman Kac and related equations
Problem solutions
Books and notes on stochastic calculus
Here are some references that to not try to be mathematicaly rigorous.
- Book by Ludwig Arnold. Clear physical discussion.
Here are some references that have more measure theory and mathematical rigor.
- Lecture notes by L. C. Evans. More emphasis on mathematical rigor.
- Book by Michael Steele. Elegant, concise, clear. Includes elementary applications in financial math.
- Book by Rick Durrett.
Sources on R and coding practice
There are many web pages on R programming. I have selected my two favorites, but you should feel free to surf the web looking for others. R is similar to Matlab and Python, but the documentation on R is far worse.
Classes that use R have pages with links (like this one).
Style in programming is important, particularly if you want your code to work. Programmers argue about style conventions, but good programmers all have them. Look at their code and see. Much of the R code posted on the web as examples has awful style. It is up to you to have higher professional standards than these hackers. This class does not use the "object oriented" parts of R. You don't have to read up on classes with style.
- One simple set of rules that I don't completely agree with.
- A post on style in the most important statistics blog there is.