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Overview
Tutorial sessions
Examination and grading regulations Last edited on
2026/07/13 by jj.

Overview

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Time and location of the lecture course:

Wednesday and Friday 11:15-12:45, MΛTHEMΛTIKON, INF 205, Hörsaal

Please register by using MaMpf and MÜSLI to receive timely announcements.

Contact:

Lecturer: Jan JOHANNES

Assistent: Bianca Neubert

Assistent: Henning Stein

Questions, please directly by email to <lehre-sip[at]math.uni-heidelberg.de>.

Language:

The lecture will be given in English if there is at least one non-German speaking participant.

Materials and announcements for the lecture:

All materials and current announcements related to the lecture can be found on MaMpf.

Registration for the tutorial sessions:

Please register for the tutorial sessions via MÜSLI an.

The tutorial sessions begin in the second week of lectures.

Read more about the tutorial sessions …

Location and time of the exams:

To be announced.

Read more about examination and grading regulations …

Lecture outline:

The outline of the lecture (chapter 1-7, sections §01-§22, 2026/07/13) is published before the lecture takes place. Before the lecture, an incomplete set of lecture notes will be made available to you on MaMpf. The complete lecture notes will be published on MaMpf shortly after the lecture. In the following table the individual documents are ordered by subjects.

		outline	notes
Chap 1	Measure and integration theory
§01	Measure theory		le01, le02
§02	Integration theory		le03, le04, le05
§03	Measures with density		le06
§04	Measures on product spaces		le07, le08
Chap 2	Conditional expectation
§05	Discretely or continuously distributed random variables
§06	Positive numerical random variables		le09, le10
§07	Integrable random variables		le11
§08	Bayesian approach		le12
Chap 3	Stochastic processes and stopping times
§09	Stochastic processes
§10	Stopping times		le13
Chap 4	Martingale theory
§11	Positive (super-)martingale		le14, le15
§12	Integrable (sub-,super-)martingale
§13	Regular integrable martingale		le16
§14	Regular stopping time for an integrable martingale		le17
§15	Regular integrable submartingale
§16	Doob decomposition and square variation		le18
Chap 5	Markov chains
§17	Markov chains		le19
§18	Recurrence und transience
§19	Invariant distribution		le20, le21
Chap 6	Ergodic theory
§20	Stationary and ergodic processes		le22
§21	Ergodic theorems		le23
Chap 7	Exponential inequalities	Chap 1-7	(2026/07/13)
§22	Exponential inequalities		le24

References:

The course does not require any additional literature, a prerequisite is the lecture course Einführung in die Wahrscheinlichkeitstheorie und Statistik (Skript). However, if you would like supplementary reading, we can recommend the following books:

• Bauer: Maß- und Integrationstheorie. (Walter de Gruyter, 2., überarbeitete Auflage, 1992).HEIDI
• Chow and Teicher: Probability Theory: Independence, Interchangeability, Martingales (Springer, 3. ed., 2003). HEIDI
• Chung: A Course in Probability Theory (Academic Press, 3. ed., 2006). HEIDI
• Durrett: Probability: Theory and Examples (Cambridge University Press, 4. ed., 2010). HEIDI
• Elstrodt: Maß- und Integrationstheorie. (Springer, 7., überarbeitete und ergänzte Auflage, 2011.) HEIDI
• Kallenberg: Foundations of Modern Probability (Springer, 3. ed., 2021). HEIDI
• Karlin and Taylor: A first course in stochastic processes (Academic Press, 2. ed., 2004). HEIDI
• Karlin and Taylor: A second course in stochastic processes (Academic Press, 14., 2005). HEIDI
• Klenke: Wahrscheinlichkeitstheorie (Springer, 4., überarbeitete und ergänzte Auflage, 2020). HEIDI
• Neveu: Martingales à temps discret (Masson, 1972). HEIDI