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Probability Theory
Last Updated: 2026-02-05 16:30:05
Abstract
Basics of probability theory and the theory of stochastic processes in discrete time
Objective
- Basic methods in probability. - Fundamental convergence theorems (law of large numbers, central limit theorem). - Introduction to discrete martingale theory and applications - Introduction to Markov chains and applications
Content
PART 1: FUNDAMENTAL RESULTS - Law of large numbers - Different notions of convergences for random variables - Characteristic functions - Convergence in law - Central limit Theorem PART 2: MARTINGALES - Conditional expectation - Almost sure convergence - Optional stopping theorem PART 3: MARKOV CHAINS - Definition, Markov property - Classification of states - Convergence to equilibrium
Resources
Lecture Notes
hand written, updated weekly and available online
Literature
J.F. Le Gall, Probability Theory, Springer 2022 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
- written 120 minutes
- Aids
- None
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Probability Theory |
|
4 h weekly |
| exercise |
Probability Theory
Groups are selected in myStudies.
Tue 14-15 or Tue 15-16 starting in the second week of the semester.
|
|
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 14 of the required 26 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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