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## Probability and Stochastic Processes

• Teacher(s):   H.Albrecher
• Course given in: English
• ECTS Credits: 6 credits
• Schedule: Autumn Semester 2019-2020, 4.0h. course (weekly average)
•  séances
•  course website
• Related programme: Master of Science (MSc) in Actuarial Science

[warning] This course syllabus is currently edited by the professor in charge. Please come back in a few days. --- For your information only, here is the old syllabus :

### 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.

### 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.

S. Cyganowski, P. Kloeden, and J. Ombach.
From elementary probability to stochastic differential equations with MAPLE.
Universitext. Springer-Verlag, Berlin, 2002.

### Evaluation

#### First attempt

Exam:
Written 3h00 hours
Documentation:
Not allowed
Calculator:
Allowed with restrictions
Evaluation:

Written Final Exam: 3h, closed-book, non-programmable calculator authorized (60% + class participation 20%+ mid-term exam 20%) Non programmable calculator only

#### Retake

Exam:
Written 3h00 hours
Documentation:
Not allowed
Calculator:
Allowed with restrictions
Evaluation:

Retake: written, 3h, closed-book, non-programmable calculator authorized (60%); other elements are the same as above Non programmable calculator only

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