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Probability and Stochastic Processes

  • Teacher(s):   M.Bladt  
  • Course given in: English
  • ECTS Credits: 6 credits
  • Schedule: Autumn Semester 2021-2022, 4.0h. course (weekly average)
  •  sessions
  • site web du cours course website
  • Related programme: Master of Science (MSc) in Actuarial Science
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Objectives

The goal is to provide a solid intuitive understanding of probability and stochastic processes. The course serves as a preparation for subsequent courses of the program.

The course will be given face-to-face in the classroom. Depending on the evolution of the COVID-19 situation, adaptations of these plans may be necessary during the semester.

Contents

Probability theory and probability calculus.

Important laws, such as the law of total probability, the rule of the iterated expectation, etc.


Moment generating functions and their applications.

Famous families of distributions.


Markov chains.

Lévy processes, in particular the Poisson process and the Wiener process.

Absolute and quadratic variation of a process

Martingales

References

P. Olofsson and M. Andersson: Probability, Statistics and Stochastic Processes. Wiley, second edition, 2012.

S.M. Ross. Introduction to probability models. Harcourt/Academic Press, Burlington, MA, seventh edition, 2000.

Evaluation

First attempt

Exam:
Written 3h00 hours
Documentation:
Allowed
Calculator:
Allowed with restrictions
Evaluation:

Written Final Exam (Online): 3h, open-book, non-programmable calculator authorized (60% + homework 20%+ mid-term exam 20%).

Depending on the evolution of the COVID-19 situation, adaptations of these plans may be necessary during the semester.

Retake

Exam:
Written 3h00 hours
Documentation:
Allowed
Calculator:
Allowed with restrictions
Evaluation:

Written exam (60%), Online, 3h, open-book, non-programmable calculator authorized

Other elements are the same as above

Depending on the evolution of the COVID-19 situation, adaptations of these plans may be necessary during the semester.



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