Ruprecht-Karls-Universität Heidelberg
Siegel der Universität Heidelberg

Module for [Scientific Computing]

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[Spatial Stochastic Processes] - [2015 Sommer]

Module Code
MH13c
Name
Spatial Stochastic Processes
Credit Points
8 CP
Workload
240 h
Duration
1 semester
Cycle
0
Methods Lecture 4 h + Exercise course 2 h
Objectives To have a firm understanding of the theory of stochastic processes on Euclidean spaces and spheres
Content • Basic notions: random functions, Kolmogorov’s theorem, Gaussian processes, stationarity, Bochner’s Theorem, Cramér’s theorem, spatial prediction • Second order theory: positive definite functions on Euclidean spaces and spheres, non-stationary schemes, spectral theory and orthogonal expansions • Gaussian random fields and Lévy bases: Properties of the sample paths, stochastic integrals • Models building and model fitting for spatial and spatiotemporal data
Learning outcomes • Firm theoretical understanding of spatial stochastic processes • Ability to build basic stochastic models for spatial data
Prerequisites
Suggested previous knowledge MC4 or equivalent;
MD2 or equivalent
Assessments TBD (typically, homework and written exam)
Literature Yaglom, A. M.: Correlation Theory of Stationary and Related Random Functions, Springer 1987
Gneiting, T. and Guttorp, P.: Continuous-parameter stochastic process theory, in Handbook of Spatial Statistics (Gelfand, A. E., Diggle, P. J., Fuentes, M. and Guttorp, P., eds.), Chapman & Hall 2010, pages 17–28
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