Univ. Heidelberg
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Ruprecht-Karls-Universität Heidelberg Statistics of inverse problems Research Group Lecture course Probability theory 1 (SS 2024)
german english


Time and location
Exercises groups
Exercises sheets
Assessment
Lecture outline
References Last edited on
2024/07/25 by jj.
Time and location of the lecture course:
Wednesday and Friday 09:15-10:45, MΛTHEMΛTIKON, INF 205, Hörsaal
Timely announcement about the lecture you receive on Moodle.
Please register by using Müsli to obtain further details by email.

Contact:
Lecturer: Prof. Dr. Jan JOHANNES <johannes[at]math.uni-heidelberg.de>
Assistent: Bianca Neubert <neubert[at]math.uni-heidelberg.de>
Questions, please directly by email or by using the contact form.

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

Exercise group:
Please register for the exercise group by using Müsli.
We propose the following exercise groups:

DayTime MΛTHEMΛTIKON (INF 205) Instructor
Thursday 09:00 - 11:00 Seminarraum 5
Friday 11:00 - 13:00 Seminarraum 5
Questions, please directly to the instructor by using Müsli.

Exercise sheets:
The Exercise sheet are published weekly on Moodle.
Please hand in your solution proposals every monday before 09:00 a.m. in the designated boxes (MΛTHEMΛTIKON, INF 205, 1st floor, in front of Dekanat) or online on Moodle.
The exercise should be handed over in fixed groups of three.
The name of the uploaded file should have the form Name1_Name2_Name3_Sheet3.pdf.
Please register by using Müsli to obtain further details by eMail.


Admission requirements and final grade:
The written examinartion will solely determine the final grade. You have to pass the written examination, in order to successfully attend the modul.

Admission requirements:
  • Accepted for the written examination is someone who either
    • has achieved at least 50% of the points of the exercises and
    • has actively participated during the exercises
  • or
    • was accepted for a written examination of a previous lecture named Probability theory 1 and has not lost the examination claim.
Grading rules:
  • Two exam dates will be offered (probably at the beginning and at the end of the lecture-free period). The 1st exam and the 2nd exam each count as one exam.
  • It is not possible to repeat a passed exam. Anyone who takes part in the first exam and passes with at least grade 4.0 cannot take part in the second exam.
  • Examinations that have not been passed or are deemed to have been failed can be repeated twice.

Lecture outline:
The outline of the lecture (chapter 1-5, sections §01-§19, 09.07.2024) is published before the lecture takes place. All lecture notes can be found as soon as possible after the lecture separately on here as well as combined Part A (le01-le09), Part B (le10-le18) and Part C (le19-le25). In the following table the individual documents are ordered by subjects.
      outline  notes
Kap 1 Measure and integration theory
§01 Measure theory le01 le02
§02 Integration theory le03 le04 le05 le06
§03 Measures with density le07
§04 Measures on product spaces le08 le09 le10
Chap 2 Conditional expectation
§05 Discretely or continuously distributed random variables
§06 Positive numerical random variables le11 le12
§07 Integrable random variables le13
§08 Bayesian approach le14
Chap 3 Stochastic processes and stopping times
§09 Stochastic processes
§10 Stopping times le15
Chap 4 Martingale theory
§11 Positive (super-)martingale le16 le17
§12 Integrable (sub-,super-)martingale
§13 Regular integrable martingale le18
§14 Regular stopping time for an integrable martingale le19
§15 Regular integrable submartingale
§16 Doob decomposition and square variation le20 le21
Chap 5 Markov chains Chap 1-5
§17 Markov chains (09.07.2024)
§18 Recurrence und transience le22
§19 Invariant distribution le23 le24 le25

References:
Bauer: Maß- und Integrationstheorie (Walter de Gruyter, 2., überarbeitete Auflage, 1992).
Chow and Teicher: Probability Theory: Independence, Interchangeability, Martingales (Springer-Verlag, 1987).
Chung: A Course in Probability Theory (Harcourt, Brace & World Inc., 1968).
Durrett: Probability: Theory and Examples (Cambridge University Press, Cambridge, 2010).
Elstrodt: Maß- und Integrationstheorie (Springer, 7., überarbeitete und ergänzte Auflage, 2011).
Kallenberg: Foundations of Modern Probability (Springer, Berlin, Heidelberg, 2002).
Karlin and Taylor: A First/Second Course in Stochastic Processes (Academic Press, San Diego, California, 2005).
A. Klenke: Probability Theory. A Comprehensive Course (Springer, Berlin, Heidelberg, 2008).
Neveu: Martingales à temps discret (Masson, 1972).
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