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Probability Theory
Last Updated: 2026-02-05 15:35:16
Abstract
Basics of probability theory and the theory of stochastic processes in discrete time
Objective
This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
Content
This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
Resources
Lecture Notes
available in electronic form.
Literature
R. Durrett, Probability: Theory and examples, Duxbury Press 1996 H. Bauer, Probability Theory, de Gruyter 1996 J. Jacod and P. Protter, Probability essentials, Springer 2004 A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006 D. Williams, Probability with martingales, Cambridge University Press 1991
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Probability Theory
The lecturers will communicate the exact lesson times of ONLINE courses.
URL for live streaming:
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4 h weekly |
| exercise |
Probability Theory
Groups are selected in myStudies.
Online class
All students will be by default enrolled in the online exercise class. Each Tuesday a recording of the exercise class will be available.
In-person classes
If you want to join an in-person class you will need to register each week for one of the classes. You will receive an email every Monday at 12:00 with a link to register for the class on Tuesday.
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1 h weekly |
Offered In
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Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Bachelor Core Courses: Applied Mathematics ... (Further restrictions apply, but in particular: 401-3601-00L Probability Theory can only be recognised for the Master Programme if neither 401-3642-00L Brownian Motion and Stochastic Calculus nor 401-3602-00L Applied Stochastic Processes has been recognised for the Bachelor Programme. 402-0205-00L Quantum Mechanics I is eligible as an applied core course, but only if 402-0224-00L Theoretical Physics (offered for the last time in FS 2016) isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office ( ) after having received the credits.)
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Statistics Master (The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.)
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