Noise convolution models: fluids in stochastic motion, nonGaussian tempospatial
fields, and a notion of tilting
Jörg Wegener
Centre for Mathematical Sciences
Mathematical Statistics
Lund University
2010
ISBN 9789174730326
LUTFMS10382010

Abstract:

The primary topic of this thesis is a class of tempospatial 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 'timereversibility' 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 tempospatial 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.


Key words:

Noise convolution models, asymmetry, nonGaussian model, tempospatial fields,
shallow water equations, generalized Laplace








