# 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 | â¢ Basic notions: random functions, Kolmogorovâs theorem, Gaussian processes, stationarity, Bochnerâs Theorem, CramÃ©râs theorem, spatial prediction â¢ Second order theory: positive definite functions on Euclidean spaces and spheres, non-stationary schemes, spectral theory and orthogonal expansions â¢ Gaussian random fields and LÃ©vy bases: Properties of the sample paths, stochastic integrals â¢ Models building and model fitting for spatial and spatiotemporal data | |||

Learning outcomes | â¢ Firm theoretical understanding of spatial stochastic processes â¢ 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 |