We will cover the followping topics.
1. Preliminary
basic probability theory, conditional expectation, convergence of random variables, basic measure theory (Lebesgue’s decomposition theorem)
2. Limit theorems
law of large numbers (weak law and strong law for i.i.d. sequence), central limit theory for i.i.d. case, introduction to large deviations
3. Stochastic process
basic concepts (sample paths, distribution), Poisson process (definition, generator, law of large numbers, CLT)
If time permits, we will also include topics on Brownian motion and point process.
Course Schedule
Mon Tue Wed Thu Fri
6/11 9-11 7/11 9-11 9/11 9-11
13/11 9-11 14/11 9-11 15/11 9-11