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Module Number:
| 13889
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| Module Title: | Stochastic Processes |
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Stochastische Prozesse
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| Department: |
Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
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| Responsible Staff Member: | -
Prof. Dr. rer. nat. habil. Wunderlich, Ralf
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Prof. Dr. rer. nat. Hartmann, Carsten
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| Language of Teaching / Examination: | English |
| Duration: | 1 semester |
| Frequency of Offer: |
Each summer semester odd year
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| Credits: |
8
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| Learning Outcome: | After successfully completing the module, students
- are familiar with the basic concepts and ideas behind random processes,
- know models and methods for time-dependent random phenomena,
- are prepared for studying advanced topics in stochastics
- have experience in autonomously doing research based on specific applications.
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| Contents: | - Markov processes, discrete and continuous in time,
- communication classes and asymptotic behaviour of Markov chains
- processes with independent and stationary increments, martingales
- stopping times and stopping theorems, optimal stopping
- applications from finance, science and engineering
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| Recommended Prerequisites: | Knowledge of the contents of module
- 11217 Wahrscheinlichkeitstheorie
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| Mandatory Prerequisites: | None |
| Forms of Teaching and Proportion: | -
Lecture
/ 4 Hours per Week per Semester
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Self organised studies
/ 180 Hours
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| Teaching Materials and Literature: | - P. Bremaud. Markov Chains, Springer, 1999.
- K.L Chung. Markov Chains: With Stationary Transition Probabilities. Springer, 2012.
- J.L. Doob: Stochastic Processes. Wiley, 1990.
- R. Durrett. Essentials of Stochastic Processes. Springer, 1999.
- S.R.S. Varadhan. Stochastic Processes. AMS, 2007.
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| Module Examination: | Final Module Examination (MAP) |
| Assessment Mode for Module Examination: | - Written examination, 90 min. OR
- Oral examination, 30 min.
In the first lecture it will be anounced, if the examination will be offered in written or oral form. |
| Evaluation of Module Examination: | Performance Verification – graded |
| Limited Number of Participants: | None |
| Part of the Study Programme: | -
Master (research-oriented) /
Angewandte Mathematik /
PO 2019
- 1. SÄ 2021
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Master (research-oriented) /
Artificial Intelligence /
PO 2022
- 1. SÄ 2024
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Bachelor (research-oriented) /
Informatik /
PO 2008
- 2. SÄ 2024
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Master (research-oriented) /
Informatik /
PO 2008
- 3. SÄ 2024
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Master (research-oriented) /
Mathematical Data Science /
PO 2025
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Master (research-oriented) /
Mathematics /
PO 2025
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Bachelor (research-oriented) /
Mathematik /
PO 2023
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Bachelor (research-oriented) - Co-Op Programme with Practical Placement /
Mathematik - dual /
PO 2023
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Bachelor (research-oriented) /
Wirtschaftsmathematik /
PO 2023
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Bachelor (research-oriented) - Co-Op Programme with Practical Placement /
Wirtschaftsmathematik - dual /
PO 2023
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| Remarks: | - Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in the complex „Stochastik“
- Study programme Mathematik B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend
- Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend
- Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Knowledge Acquisition, Representation, and Processing“
- Study programme Informatik B.Sc.: Compulsory elective module in field of application „Mathematik“
- Study programme Informatik M.Sc.: Compulsory elective module in field of application „Mathematik“
- Study programme Mathematics M.Sc.: Compulsory elective module in complex „Stochastics“
- Study programme Mathematical Data Science M.Sc.: Compulsory elective module in complex „Advanced Mathematical Methods in Data Science“
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| Module Components: | - Lecture: Stochastic Processes
- Accompanying exercise
- Related examination
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| Components to be offered in the Current Semester: | |
