First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
INTRODUCTION TO STOCHASTIC PROCESSES
SCO2046352, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20
N0
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination INTRODUCTION TO STOCHASTIC PROCESSES
Website of the academic structure http://matematica.scienze.unipd.it/2019/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
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

Lecturers
Teacher in charge MARCO FORMENTIN MAT/06

Mutuating
Course unit code Course unit name Teacher in charge Degree course code
SCP4063083 STOCHASTIC PROCESSES MARCO FORMENTIN SS1736

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2011 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)

Syllabus
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.
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, Probabilità. Un'introduzione attraverso modelli e applicazioni. --: Springer Verlag, 2013. Cerca nel catalogo