Course 2020-2021 a.y.

20604 - STOCHASTIC PROCESSES

Department of Decision Sciences

Course taught in English
Go to class group/s: 31
DSBA (8 credits - I sem. - OBCUR  |  SECS-S/01)
Course Director:
ANTONIO LIJOI

Classes: 31 (I sem.)
Instructors:
Class 31: ANTONIO LIJOI


Class-group lessons delivered  on campus

Suggested background knowledge

The course is self-contained, though prior knowledge of the contents of an intermediate Probability Theory course may be helpful.

Mission & Content Summary

MISSION

The course introduces students to advanced topics in modern Probability Theory that are essential for modeling time dependent random phenomena. The first part focuses on some introductory topics in measure-theoretic probability that include expectations, independence, classical limit theorems, conditional expectation and conditional probabilities. The second part focuses on discrete and continuous time stochastic processes that are relevant in Statistics and Machine Learning applications.

CONTENT SUMMARY

  1. Some useful notions and results from Measure Theory.
  2. Probability spaces, random variables and random vectors. Expectations and  spaces. Independence.
  3. Convergence of sequences of random variables. Laws of Large Numbers and Central Limit Theorems.
  4. Conditional expectations in L1 and in L2 spaces. Conditional probabilities.
  5. Filtrations and stopping times. Martingales.
  6. Poisson random measures.
  7. Lévy processes.
  8. Brownian motion.

Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Deal with advanced mathematical tools that lie at the foundations of modern probabilistic applications in Data Science.
  • Gain a deep understanding of stochastic models that are used to describe complex dependence structures occurring in real world applications.
  • Profitably attend graduate courses on advanced topics in Statistics and Machine Learning.

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Address modeling of the time evolution of random phenomena in a rigorous probabilistic framework.
  • Master the interplay between probability theory and advanced modeling tools used in Statistics and Machine Learning.

Teaching methods

  • Face-to-face lectures

DETAILS

  


Assessment methods

  Continuous assessment Partial exams General exam
  • Oral individual exam
    x

ATTENDING AND NOT ATTENDING STUDENTS

The assessment consists of two oral individual exams:

  1. An oral exam on the first part of the course, which coincides with topics 1.-4. in the course content summary. The mark of this part receives a weight equal to 0.35 for determining the final overall mark.
  2. An oral exam on the second part of the course, which covers topics 5.-8. in the course content summary. The mark of this part receives a weight equal to 0.65 for determining the final overall mark.
  • The exam aims at ascertaining students’ understanding of the stochastic processes theory and of the specific examples that are developed during lectures for illustrating the applications of the most relevant mathematical results.
  • There are no different assessment methods or exam programs for attending and non-attending students.

Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

E. CINLAR, Probability and Stochastics. Springer, New York, 2011.

Last change 21/07/2020 14:55