Course description and contents
We intend to go through the core stochastic processes. If time permits, we will talk about more advanced topics. We will try to emphasize the intuition that is underlying the main ideas: the topics will roughly cover:
- Random walks: evolution, ballot theorems, fluctuations.
- Discrete time Markov chains: evolution, convergence, hitting time, cover time.
- Continous time Markov chains.
- Poisson process and the exponential distribution.
- Branching processes: the Galton--Watson process, age-dependent processes.
- Concentration: exponential concentration, martingale methods.
- Renewal theory.