### Lecture notes

- Week 2, Discrete probability, discrete Markov chains
- Week 3, Continuous time, Brownian motion and OU
- Week 4, Brownian Motion and the heat equation
- Week 5, Ito integral with respect to Brownian motion
- Week 6, Ito's Lemma and some backward equations for Brownian motion
- Week 7, General diffusions, Poisson process, backward equation
- Week 8, General diffusions, part 2: Ito calculus (incomplete)
- Week 9, Forward equation, generator, duality
- Week 10, Change of measure, Girsanov

### 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.