VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

401-3601-00L 10 Credits BSC , MSC D-MATH
You're viewing possible stale or outdated data. Please check the latest semester for more up-to-date information.

Probability Theory

Wahrscheinlichkeitstheorie

Lecturers & Examiners: Prof. Dr. Martin Schweizer
VVZ CR 4.2

Last Updated: 2026-02-05 15:05:36

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 - Probability measures on product spaces (stochastic kernels, Ionescu-Tulcea theorem) - Conditional expectations - Martingales (stopping times, stopping theorem, convergence theorems, applications) - Weak convergence (Prohorov's theorem, characteristic functions) - perhaps Brownian motion and Donsker's theorem

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 - Probability measures on product spaces (stochastic kernels, Ionescu-Tulcea theorem) - Conditional expectations - Martingales (stopping times, stopping theorem, convergence theorems, applications) - Weak convergence (Prohorov's theorem, characteristic functions) - perhaps Brownian motion and Donsker's theorem

Resources

Lecture Notes

available, will be sold in the course

Literature

R. Durrett, Probability: Theory and examples, Duxbury Press 1996 J. Jacod and P. Protter, Probability essentials, Springer 2004 A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006 J. Neveu, Bases mathematiques du calcul des probabilites, Masson 1980 D. Williams, Probability with martingales, Cambridge University Press 1991

General Information

Language
German
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Wahrscheinlichkeitstheorie
  • Tue 10:15-12:00 (HG D 5.2)
  • Thu 10:15-12:00 (HG E 41)
4 h weekly
exercise Wahrscheinlichkeitstheorie
  • Tue 14:15-15:00 (HG D 5.3)
  • Tue 14:15-15:00 (HG F 26.1)
  • Wed 13:15-14:00 (HG D 5.3)
  • 01.11 Date 13:15-14:00 (HG D 5.1)
  • 03.01 Date 12:15-14:00 (HG D 5.1)
1 h weekly

Offered In