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Noise Convolution Models: Fluids in Stochastic Motion, Non-Gaussian Tempo-Spatial Fields, and a Notion of Tilting

Wegener, Jörg LU (2010) In Doctoral Theses in Mathematical Sciences 2010:8.
Abstract
The primary topic of this thesis is a class of tempo-spatial models which

are rather flexible in a distributional sense. They prove quite successful

in modeling (temporal) dependence structures and go beyond the limitation of Gaussian models, thus allowing for heavy tails and skewness.

By generalizing the construction of the above class of models, it is possible to ‘control’ some random geometric features of the sample path

– while keeping the covariance function unaltered. Features such as

horizontal and vertical asymmetries (including the question of ‘time-

reversibility’ in financial context) and tilting of trajectories. These properties are most prominent in the extremes of the... (More)
The primary topic of this thesis is a class of tempo-spatial models which

are rather flexible in a distributional sense. They prove quite successful

in modeling (temporal) dependence structures and go beyond the limitation of Gaussian models, thus allowing for heavy tails and skewness.

By generalizing the construction of the above class of models, it is possible to ‘control’ some random geometric features of the sample path

– while keeping the covariance function unaltered. Features such as

horizontal and vertical asymmetries (including the question of ‘time-

reversibility’ in financial context) and tilting of trajectories. These properties are most prominent in the extremes of the process (but do not exist

in e.g. Gaussian models) as shown by means of Rice’s formula for level

crossings. Different measures for assessing asymmetries in data records

are proposed and model fitting procedures discussed.

To combine stochastic and deterministic modeling in the context of numerical weather prediction, we present randomized versions of ‘simple’

physical models based on the shallow water equations. By embedding

deterministic shallow water motion into a Gaussian tempo-spatial convolution model, one obtains a velocity field that can be interpreted as

stochastically distorted shallow water flow. The methodology is meant

to provide prediction, estimation and the handling of uncertainties on

various scales. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Docent Seleznev, Oleg, Umeå University, Umeå
organization
publishing date
type
Thesis
publication status
published
subject
keywords
generalized Laplace, shallow water equations, asymmetry, noise convolution models, tempo-spatial fields, non-Gaussian model
in
Doctoral Theses in Mathematical Sciences
volume
2010:8
pages
141 pages
publisher
Mathematical Statistics, Centre for Mathematical Sciences, Lund University
defense location
Lecture hall MH:C, Center of Mathematics, Sölvegatan 18, Lund University Faculty of Engineering
defense date
2010-11-12 10:15
ISSN
1404-0034
language
English
LU publication?
yes
id
d9eb581c-d72f-44ea-85e8-e32aa136b738 (old id 1691468)
date added to LUP
2010-10-19 12:59:27
date last changed
2018-05-29 09:49:04
@phdthesis{d9eb581c-d72f-44ea-85e8-e32aa136b738,
  abstract     = {The primary topic of this thesis is a class of tempo-spatial models which<br/><br>
are rather flexible in a distributional sense. They prove quite successful<br/><br>
in modeling (temporal) dependence structures and go beyond the limitation of Gaussian models, thus allowing for heavy tails and skewness.<br/><br>
By generalizing the construction of the above class of models, it is possible to ‘control’ some random geometric features of the sample path<br/><br>
– while keeping the covariance function unaltered. Features such as<br/><br>
horizontal and vertical asymmetries (including the question of ‘time-<br/><br>
reversibility’ in financial context) and tilting of trajectories. These properties are most prominent in the extremes of the process (but do not exist<br/><br>
in e.g. Gaussian models) as shown by means of Rice’s formula for level<br/><br>
crossings. Different measures for assessing asymmetries in data records<br/><br>
are proposed and model fitting procedures discussed.<br/><br>
To combine stochastic and deterministic modeling in the context of numerical weather prediction, we present randomized versions of ‘simple’<br/><br>
physical models based on the shallow water equations. By embedding<br/><br>
deterministic shallow water motion into a Gaussian tempo-spatial convolution model, one obtains a velocity field that can be interpreted as<br/><br>
stochastically distorted shallow water flow. The methodology is meant<br/><br>
to provide prediction, estimation and the handling of uncertainties on<br/><br>
various scales.},
  author       = {Wegener, Jörg},
  issn         = {1404-0034},
  keyword      = {generalized Laplace,shallow water equations,asymmetry,noise convolution models,tempo-spatial fields,non-Gaussian model},
  language     = {eng},
  pages        = {141},
  publisher    = {Mathematical Statistics, Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  series       = {Doctoral Theses in Mathematical Sciences},
  title        = {Noise Convolution Models: Fluids in Stochastic Motion, Non-Gaussian Tempo-Spatial Fields, and a Notion of Tilting},
  volume       = {2010:8},
  year         = {2010},
}