
Course unit
INTRODUCTION TO STOCHASTIC PROCESSES
SCO2046352, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/06 
Probability and Mathematical Statistics 
8.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
8.0 
64 
136.0 
No turn 
Prerequisites:

A basic course in Probability 
Target skills and knowledge:

Good knowledge of the theory of the discrete time and continuous Markov models. Ability to solve advanced problems and exercises related to these processes. 
Examination methods:

Written examination with exercises for solution similar to those solved in class. Statements and proofs of relevant theorems may be also asked. 
Assessment criteria:

Student must be familiar with theory of Markov processes and be able to solve exercises of appropriate difficulty. 
Course unit contents:

Definition of Stochastic process. Probability and conditional expectation. Conditional independence.
Discretetime Markov chains: basic definitions, transition matrix, Markov property, Random Walk and its properties, absorption probabilities, stopping times, strong Markov property, classification of the states,
periodicity, invariant distributions, Ergodic theorem.
Gibbs fields and Monte Carlo Simulation. Basics of Large Deviations.
Poisson process: main properties and applications.
Continuoustime Markov chains: basic definitions, generator matrix, Jump chain and holding times, absorption probabilities, classification of the states, invariant distribution, Ergodic theorem.
Applications: Birth and death process, Queues and queueing networks. 
Planned learning activities and teaching methods:

Taught lessons: theory (34 hours) exercises (30 hours) 
Additional notes about suggested reading:

All the topics of the course will illustrated in class. Additional material (exercises and notes) will be available on moodle. 
Textbooks (and optional supplementary readings) 

Pierre Bremaud, Markov Chains, Gibbs Fields, Monte Carlo Simulation and queues. : Springer, 1998.

Frank den Hollander, Large deviations. : , 2000.

Paolo Dai Pra, Francesco Caravenna, Probabilità. Un'introduzione attraverso modelli e applicazioni. : Springer Verlag, 2013.


