Probability Theory

Lecture Probability Theory


LecturerProf. Dr. Ulrich Stadtmüller
Class Teacher
Christian Hering
Type of Lecture 2 h Lecture, 1 h Class (2+1)
Venue and Time
  • Monday, 10-12 in H13
  • Wednesday, 4p-6p in H14 (biweekly)
  • Conditional Expectation and conditional probability
  • Time-discrete Martingals
    • Essentials
    • Stopping Times
    • Optional Sampling Theorems
    • Stochastic Inequalities
    • Doobs Martingale Theorem
    • Uniform Integrability of Martingals
    • Strong Law of Large Numbers
    • Large Deviations
    • Applications
  • The lecture notes are available here.
  • This lecture consists out of two parts. Information about the other part of the lecture (held by Prof. Schmidt) can be found here.
  • If you do not have a SLC login, please set up a SLC-Account as soon as possible.
  • Exercise sheets are due Wednesday before class.
  • The lecture as well as the class will be in German.
Excersise Sheets
  • Heinz Bauer, Wahrscheinlichkeitstheorie,
    de Gruyter, 2002
  • Patrick Billingsley, Probability and Measure,
    Wiley, 1986
  • Richard Durrett, Probability:Theory and Examples,
    Duxbury Press, 1996
  • Peter Gänssler, Winfried Stute, Wahrscheinlichkeitstheorie,
    Springer, 1977
  • Allan Gut, Probability: A Graduate Course,
    Springer 2005
  • Olav Kallenberg, Foundations of Modern Probability, Springer, 2002
  • Albert N. Sirjaev, Probability,
    Springer, 1996
  • David Williams, Probability with Martingales,
    Cambridge University Press, 2005
Download the list as <link fileadmin website_uni_ulm mawi.inst.zawa lehre literatur.pdf download>pdf.


Prof. Dr. Ulrich Stadtmüller
Office Hours: By Appointment
Phone: +49 (0)731/ 50-23512
Ulrich Stadtmüller

Class Teacher
Christian Hering
Office Hours: By Appointment
Phone: +49 (0)731/ 50-23514
Christian Hering


  • The certificates for this lecture can be picked up in my office (He18 | 206).
  • The lecture notes are not completed yet, I will inform the students of this lecture by Email as soon as they are.
  • The lecture notes for the whole period are online now. It is a preliminary version which was not proofread yet. I appreciate any comments on it.

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