14267 - Advanced Topics of Stochastics Modulübersicht

Module Number: 14267
Module Title:Advanced Topics of Stochastics
  Fortgeschrittene Themen der Stochastik
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. Hartmann, Carsten
  • Prof. Dr. rer. nat. habil. Wunderlich, Ralf
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 6
Learning Outcome:After successfully completing the module, students have in-depth knowledge in the field of stochastics. They are able to assess the aims and scope of probability models and related numerical methods. Using specific applications, students have gained experience in independent scientific work.
Contents:Course topics include (but are not limited to):
  • stochastic simulation (e.g. Markov Chain Monte Carlo, simulated annealing, sensitivity analysis)
  • time series analysis (e.g. regression models, autoregressive processes, estimation and prediction)
  • uncertainty quantification (e.g. entropy and information, inverse problems, Kalman filters)
  • Monte Carlo methods for partial differential equations (e.g., diffusion processes Feynmac-Kac formulae)
  • modelling extreme events (z.B. extreme value theory, large deviations, theory of risk)
Recommended Prerequisites:Knowledge of the contents of modules
  • 11217: Wahrscheinlichkeitstheorie,
  • 11103: Analysis I,
  • 11104: Analysis II and
  • 11101: Lineare Algebra and Analytische Geometrie I
or good knowledge of the contents of modules
  • 11917: Mathematik W-3 (Statistik) or 11217: Wahrscheinlichkeitstheorie
  • 11213: Mathematik IT-3 (Analysis) and
  • 11113: Mathematik IT-2 (Lineare Algebra)
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 3 Hours per Week per Semester
  • Exercise / 1 Hours per Week per Semester
  • Self organised studies / 120 Hours
Teaching Materials and Literature:
  • S. Asmussen, P.W. Glynn. Stochastic Simulation: Algorithms and Analysis, Springer, 2007.
  • P.J. Brockwell, R.A. Davis. Introduction to Time Series and Forecasting. Springer, 2010.
  • E. Pardoux. Markov Processes and Applications, Wiley, 2008.
  • S. Reich, C. Cotter. Probabilistic Forecasting and Bayesian Data Assimilation. Cambridge University Press, 2015.
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of exercises
Final module examination:
  • Oral examination, 30 min.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • no assignment
Remarks:
  • Study programme Mathematics M.Sc.: Compulsory elective module in the complex „Stochastics“
  • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
  • Study programme Wirtschaftsmathematics B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
  • Study programme Informatik B.Sc.: Compulsory elective module in complex „Mathematik“.
  • Study programme Infromatik M.Sc.: Compulsory elective module in complex „Mathematik“ or in field of application „Mathematik“
Module Components:
  • Lecture: Advanced Topics in Stochastics
  • Accompanying exercises
  • Related Examination
Components to be offered in the Current Semester:
  • no assignment