Probability Theory (4V+2U, 9.0 LP)
|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|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. in WiSe|
|Level|| Bachelor (Specialization)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-STO] Stochastics/Statistics/Financial Mathematics|
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.
- 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.
- H. Bauer: Probability Theory,
- P. Billingsley: Probability and Measure,
- P. Gänssler, W. Stute: Wahrscheinlichkeitstheorie,
- A. Klenke: Wahrscheinlichkeitstheorie.
Further literature will be announced in the lecture; Exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-14-M-3] Stochastic Methods (M, 9.0 LP)
Requirements for attendance (formal)
References to Course [MAT-60-11-K-4]
|[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|
|[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.)|