Here is the

The midterm will be on March 9th and the final on May 4th during class.

They will account for respectively 30 and 50 percent of the final grade, another 20 percent will come from the homework.

Sketch of program

- Lecture 1 : Probability space

- Lecture 2 : Random variables (Homework)

- Lecture 3 : Definition of expectation and Galton-Watson (Homework)

- Lecture 4 : Basic properties of expectations and expectations of basic random variables. A first law of large numbers (Homework)
- Lecture 5 : Continuous random variables (Homework)

- Lecture 6 : Convergence of random variables (Homework)

- Lecture 7 :Conditional expectation and Markov chains

- Lectures 8 & 9 Markov chains.

- Lectures 10 & 11 & 12 Martingales and diffusions (Brownian motion)