Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-64-14-M-7

Numerics of Stochastic Processes (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-64-14-M-7 Numerics of Stochastic Processes 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-SPAS] Analysis and Stochastics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-64-14-K-7
Numerics of Stochastic Processes
P 42 h 93 h - - PL1 4.5 irreg.
  • About [MAT-64-14-K-7]: Title: "Numerics of Stochastic Processes"; Presence-Time: 42 h; Self-Study: 93 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86345 ("Numerics of Stochastic Processes")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Stochastic processes with a multidimensional continuous parameter space, which are called random fields, are used to model random spatial (and temporal) phenomena. Topics of the course are:
  • classical examples of random fields: Brownian sheet and Lévy's Brownian motion,
  • Hilbert spaces with reproducing kernel,
  • isotropy and stationarity of random fields,
  • regularity and approximation of random fields, series representations,
  • sparse grids and Smolyak's algorithm.

Competencies / intended learning achievements

Upon successful completion of this module, the students have gained advanced knowledge of the theory, approximation and simulation of random fields. Moreover, they have gained an exemplary insight into applications (geostatistics, fluid dynamics). They are able to name the main propositions of the lecture, classify and explain the illustrated connections. They understand the proofs and are able to reproduce and explain them.

By solving the given exercise problems, they have gained a precise and independent handling of the terms, propositions and methods of the lecture. In addition, they have learned to apply the methods to new problems, analyze them and develop solution strategies.

Literature

  • K. Ritter: Average Case Analysis of Numerical Problems.

Registration

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

References to Module / Module Number [MAT-64-14-M-7]

Module-Pool Name
[MAT-70-MPOOL-7] Specialisation Stochastic Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)