401-3601-00L  Probability Theory

SemesterAutumn Semester 2020
LecturersA.‑S. Sznitman
Periodicityyearly recurring course
Language of instructionEnglish
CommentAt most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office (Link) after having received the credits.



Courses

NumberTitleHoursLecturers
401-3601-00 VProbability Theory
The lecturers will communicate the exact lesson times of ONLINE courses.
URL for live streaming: Link
4 hrs
Tue10:00-12:00ON LI NE »
Thu10:00-12:00ON LI NE »
A.‑S. Sznitman
401-3601-00 UProbability Theory
Groups are selected in myStudies.
Online class
All students will be by default enrolled in the online exercise class. Each Tuesday a recording of the exercise class will be available.
In-person classes
If you want to join an in-person class you will need to register each week for one of the classes. You will receive an email every Monday at 12:00 with a link to register for the class on Tuesday.
1 hrs
Tue13:15-14:00ETZ E 6 »
13:15-14:00ML H 41.1 »
14:15-15:00ML H 41.1 »
A.‑S. Sznitman

Catalogue data

AbstractBasics of probability theory and the theory of stochastic processes in discrete time
ObjectiveThis 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, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
ContentThis 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, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
Lecture notesavailable in electronic form.
LiteratureR. 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

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits10 credits
ExaminersA.-S. Sznitman
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 30 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkInformation
Only public learning materials are listed.

Groups

401-3601-00 UProbability Theory
GroupsG-ON 01
G-02
Tue13:15-14:00ETZ E 6 »
G-03
Tue13:15-14:00ML H 41.1 »
G-06
Tue14:15-15:00ML H 41.1 »

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Data Science MasterCore ElectivesWInformation
Mathematics BachelorCore Courses: Applied Mathematics and Further Appl.-Oriented FieldsWInformation
Mathematics MasterBachelor Core Courses: Applied Mathematics ...E-Information
Physics BachelorSelection of Higher Semester CoursesWInformation
Physics MasterSelection: MathematicsWInformation
Statistics MasterStatistical and Mathematical CoursesWInformation
Statistics MasterSubject Specific ElectivesWInformation