240081 Wahrscheinlichkeitstheorie I (V) (WiSe 2014/2015)

Contents, comment

Die Vorlesung behandelt die wichtigsten Konzepte und Resultate der Wahrscheinlichkeitstheorie, u.a.
- Unabhängigkeit,
- unendliche Produktmaße,
- Verteilungskonvergenz,
- charakteristische Funktionen,
- Grenzwertsätze für Summen unabhängiger Zufallsgrößen
(Gesetz der großen Zahlen, Zentraler Grenzwertsatz),
- (abstrakter) bedingter Erwartungswert,
- Grundlagen der stochastischen Prozesse,
- Martingale,
- Brown'sche Bewegung.

Requirements for participation, required level

Gute Kenntnisse der Maß- und Integrationstheorie (Maß, Integral (nach Lebesgue), Konvergenzsätze, endliche Produktmaße, Satz von Fubini, Transformationsformel, L^p-Räume) sind absolut notwendig.

Grundkenntnise der Stochastik sind hilfreich, aber nicht notwendig.

Teaching staff

Dates ( Calendar view )

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Examinations

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Subject assignments

Module Course Requirements  
24-E2 Supplementary Module Mathematics 2 Ergänzungsmodul Mathematik 2 Vorlesung Student information
24-M-P1 Profile Module 1 Profilierung 1 Profilierungsvorlesung (mit Übung) - Typ 1 Student information
24-M-P2 Profile Module 2 Profilierung 2 Profilierungsvorlesung (mit Übungen) - Typ 1 Student information
24-M-PWM Profile Module Economic Mathematics Profilierung Wirtschaftsmathematik Profilierungsvorlesung (mit Übung) - Typ 1 Student information
- Graded examination Student information
24-M-SV1-SO Foundations in Stochastics and Optimisation Spezialisierung/Vertiefung 1 - Stochastik und Optimierung Spezialisierungskurs Stochastik / Optimierung Graded examination
Student information
24-M-SV1-ST Foundations in Stochastics Spezialisierung/Vertiefung 1 - Stochastik Spezialisierungskurs Stochastik Graded examination
Student information
24-M-VM1 Advanced Mathematics 1 Vertiefung Mathematik 1 Vertiefungskurs Mathematik 1 - Variante 1 Student information
- Graded examination Student information
24-SE Structured Electives Strukturierte Ergänzung Vorlesung 1 Student information
Vorlesung 2 Student information

The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.

Degree programme/academic programme Validity Variant Subdivision Status Semester LP  
Mathematik / Diplom (Enrollment until SoSe 2008) Wahlpflicht 4. 5. 6. HS
Studieren ab 50    
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WS2014_240081@ekvv.uni-bielefeld.de
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Last update basic details/teaching staff:
Tuesday, November 29, 2016 
Last update times:
Thursday, March 5, 2015 
Last update rooms:
Thursday, March 5, 2015 
Type(s) / SWS (hours per week per semester)
lecture (V) / 4
Department
Faculty of Mathematics
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48685931