Random walks 
Exercises on: Markovianity, temporal and spatial invariance, random walks with reflecting and absorbing barriers, reflection principle, ballot theorem, distribution of the maximum, hitting time theorem, first and second arc sine law, random walks and generating functions.    

Brownian motion  
Exercises on: path properties of Brownian motion, Brownian motion as a strong Markov process, transience and recurrence. 

Branching processes 
Exercises on: expectation and variance of the population size, probability of extinction of the population.   
   

Markov chains 
Exercises on: transition matrix, classification of states, classification of chains, stationary distribution and limit theorem, chains with finitely many states.  

Poisson processes 
Exercises on the main properties of Poisson processes.