This course is designed to review basic concepts in probability and to introduce to topics in stochastic processes which are expecially relevant for applications involving discrete quantities, eg counts.

1. Recap of basic probability. Probability space, random variables,
expectation, notable distributions, joint distribution,
conditioning (Ross ch. 1-3); Simulation: inverse method, rejection
method, variance reduction, point processes (Ross ch. 11). [15 h]

2. Markov chains, discrete time. transitions, classification of
states, stationarity and ergodicity, time reversibility,
Monte-Carlo-Markov-Chain methods. Examples. (Ross ch 4). [10 h]

3. Poisson process: equivalent definitions, generalizations
(non-homogeneous, compound, mixed). Examples. (Ross ch 5). [10 h]

4. Markov chains, continuous time. Transitions, birth and death
processes, reversibility. (Ross ch 6). [15 h]

5. Topics in renewal theory. (Ross ch 7-8). [10 h]

Sheldon N. Ross "Probability Models" 8th ed Academic Press

Other suggested readings:

Sheldon N. Ross "Stochastic processes" 2nd ed John Wiley

Pierre Bre'maud "Markov Chains, Gibbs Fields, Monte Carlo
Simulation and Queues" Springer 1999

Written examination.