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|Title: ||Needlet analysis of spherical random fields|
|Authors: ||Marinucci, Domenico|
|Keywords: ||spherical random fields|
high frequency asymptotics
cosmic microwave background radiation
|Issue Date: ||3-Sep-2009 |
|Abstract: ||This thesis is a collection of essays on spherical wavelets and their applications
on statistical models. In particular, its aim is to investigate a form of second generation
wavelets on the sphere called needlets, and their statistical applications to the analysis
of isotropic spherical random fields. These methods are strongly motivated by many
applications, especially from Cosmology and Astrophysics; in particular, the analysis
of so-called Cosmic Microwave Background (CMB) radiation.
Chapter 1 is to introduce the physical background and motivations of this thesis.
We will emphasize on the nature of CMB, and the statistical challenges in this field.
The concept of needlet is introduced in Chapter 2. This chapter is also preliminary
to all the remaining work we have done. It includes the introduction of continuous
and discrete spherical wavelets, isotropic spherical random fields, and the diagram formulae,
i.e. the basic ingredients that will be needed in the following cha...|
|Appears in Collections:||Tesi di dottorato in scienze matematiche e fisiche|
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