Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-60-11-K-4

Probability Theory (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
4 V Lecture 6.0 CP 56 h 124 h
2 U Exercise class (in small groups) 3.0 CP 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in WiSe
Level [4] Bachelor (Specialization)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Livecycle-State [NORM] Active

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
  • Examination number (Study achievement): 84030 ("Exercise Class Probability Theory")
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

  • Types of convergence (stochastic, almost sure, weak, L_p-convergence, convergence in distribution),
  • Characteristic functions,
  • Sums of independent random variables,
  • Strong laws of large numbers, variants of the central limit theorem,
  • Conditional expectation,
  • Martingales in discrete time,
  • Brownian motion.

Competencies / intended learning achievements

The students have acquired in-depth knowledge in stochastics and foundations for research in the field of stochastic processes. The contents of the course form the basis for all further courses in the field of stochastics and financial mathematics in the master's programmes Mathematics, Business Mathematics and Mathematics International.

Literature

  • H. Bauer: Probability Theory,
  • P. Billingsley: Probability and Measure,
  • P. Gänssler, W. Stute: Wahrscheinlichkeitstheorie,
  • A. Klenke: Wahrscheinlichkeitstheorie.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

References to Course [MAT-60-11-K-4]

Module Name Context
[MAT-30-10L-M-5] Specialisation Module (Teachers Training Programme Mathematics) WP: Obligation to choose in Obligatory-Modulteil #A (Lectures) 4V, 6.0 LP
[MAT-60-11-M-4] Probability Theory P: Obligatory 4V+2U, 9.0 LP
Course-Pool Name
[MAT-50-4V-KPOOL-4] Elective Courses Optimisation and Stochastics (4V, B.Sc.)
[MAT-50-KPOOL-4] Specialisation Optimisation and Stochastics (B.Sc.)
[MAT-70-4V-KPOOL-4] Elective Courses Analysis and Stochastics (4V, B.Sc.)
[MAT-70-KPOOL-4] Specialisation Analysis and Stochastics (B.Sc.)