


Politecnico di Torino  
Academic Year 2010/11  
02KRROC, 02KRROT, 02KRRPE Stochastic processes 

Master of sciencelevel of the Bologna process in Computer And Communication Networks Engineering  Torino Master of sciencelevel of the Bologna process in Telecommunications Engineering  Torino Master of sciencelevel of the Bologna process in Nanotechnologies For Icts  Torino/Grenoble/Losanna 





Esclusioni: 02JSH 
Subject fundamentals
The course is taught in English.
The purpose of this course is to review the basic concepts of probability theory and to introduce to the theory of the stochastic processes which are especially relevant in telecommunication and computer engineering. The most relevant stochastic processes in discrete and continuous time and space are described, together with a comprehensive list of examples of application. 
Expected learning outcomes
The knowledge obtained through this course consists on the basic theory of those stochastic processes that are useful to describe and solve problems characterized by nondeterministic time evolutions and unknown behavior of lifetime of items or systems.
At the end the course the students will be able to describe and provide simple probabilistic models in queues, network or software reliability problems, and to solve them both from analytical and numerical methods. They will be also able to understand which of the presented processes is more appropriate in the analysis they have to perform, and the meaning of the values assumed by the mathematical objects presented during the lectures. The ability to apply the gained knowledge will be verified through class exercises. 
Prerequisites / Assumed knowledge
A basic knowledge of calculus and a first course in probability theory are the prerequisites for this course.

Contents
' Recap of basic probability: probability spaces, random variables and notable distributions, expectations, conditioning (10 hours)
' Poisson process: equivalent definitions, generalizations (nonhomogeneous, compound, mixed) (10 hours) ' Renewal processes: equilibrium distributions and stationary processes (10 hours) ' Discrete time Markov chains: transition matrices, classification of states, stationarity and ergodicity, time reversibility, techniques for aggregation of states (12 hours) ' Continuous time Markov chains: transitions, birth and death processes, Yule processes, branching processes (10 hours) ' SemiMarkov processes (4 hours) ' Brownian motions: definitions, properties, applications (4 hours) 
Delivery modes
Exercises will be presented and solved in the class.

Texts, readings, handouts and other learning resources
Sheldon N. Ross "Stochastic processes" 2nd ed John Wiley
Other suggested readings: Sheldon N. Ross "Probability Models" 8th ed Academic Press Pierre Bremaud "Markov Chains, Gibbs Fields, Monte Carlo Simulation and Queues" Springer 1999 
Assessment and grading criteria
Written examination.

