First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP4063083, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
SS1736, Degree course structure A.Y. 2014/15, A.Y. 2018/19
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination STOCHASTIC PROCESSES
Website of the academic structure
Department of reference Department of Statistical Sciences
E-Learning website
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge MARCO FORMENTIN MAT/06

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/06 Probability and Mathematical Statistics 9.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 9.0 64 161.0 No turn

Start of activities 01/10/2018
End of activities 18/01/2019
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
6 Commissione a.a.2019/20 01/10/2019 30/09/2020 FORMENTIN MARCO (Presidente)
BARBATO DAVID (Membro Effettivo)
CELANT GIORGIO (Membro Effettivo)
CESARONI ANNALISA (Membro Effettivo)
5 Commissione a.a.2018/19 01/10/2018 30/09/2019 FORMENTIN MARCO (Presidente)
BARBATO DAVID (Membro Effettivo)
CELANT GIORGIO (Membro Effettivo)
CESARONI ANNALISA (Membro Effettivo)

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
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.
Discrete-time 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.
Continuous-time 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. Cerca nel catalogo
  • Frank den Hollander, Large deviations. --: --, 2000. Cerca nel catalogo
  • Paolo Dai Pra, Francesco Caravenna, Probabilit√†. Un'introduzione attraverso modelli e applicazioni. --: Springer Verlag, 2013. Cerca nel catalogo