13889 - Stochastic Processes Modulübersicht

Module Number: 13889
Module Title:Stochastic Processes
  Stochastische Prozesse
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Wunderlich, Ralf
  • Prof. Dr. rer. nat. Hartmann, Carsten
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: Each summer semester odd year
Credits: 8
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.
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
Recommended Prerequisites:Knowledge of the contents of module
  • 11217 Wahrscheinlichkeitstheorie
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Self organised studies / 180 Hours
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.
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
  • Master (research-oriented) / Artificial Intelligence / PO 2022
  • Bachelor (research-oriented) / Informatik / PO 2008 - 1. SÄ 2017
  • Master (research-oriented) / Informatik / PO 2008 - 2. SÄ 2017
  • Bachelor (research-oriented) / Mathematik / PO 2019
  • Bachelor (research-oriented) / Mathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Mathematik - dual / PO 2023
  • Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2023
  • Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Wirtschaftsmathematik - dual / PO 2023
Remarks:
  • Study programme Applied Mathematics M.Sc.: Compulsory elective module in the complex „Stochastics“
  • Study programme Mathematics B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend
  • Study programme Economathematics 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“
Module Components:
  • Lecture: Stochastic Processes
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester:
  • no assignment