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Lining Liu PhD thesis.PDF441.63 kBAdobe PDFView/Open
Title: Stable and multistable processes and localisability
Authors: Liu, Lining
Supervisors: Falconer, K. J.
Keywords: Multistable
Issue Date: 23-Jun-2010
Abstract: We first review recent work on stable and multistable random processes and their localisability. Then most of the thesis concerns a new approach to these topics based on characteristic functions. Our aim is to construct processes on R, which are α(x)-multistable, where the stability index α(x) varies with x. To do this we first use characteristic functions to define α(x)-multistable random integrals and measures and examine their properties. We show that an α(x)-multistable random measure may be obtained as the limit of a sequence of measures made up of α-stable random measures restricted to small intervals with α constant on each interval. We then use the multistable random integrals to define multistable random processes on R and study the localisability of these processes. Thus we find conditions that ensure that a process locally ‘looks like’ a given stochastic process under enlargement and appropriate scaling. We give many examples of multistable random processes and examine their local forms. Finally, we examine the dimensions of graphs of α-stable random functions defined by series with α-stable random variables as coefficients.
Type: Thesis
Publisher: University of St Andrews
Appears in Collections:Pure Mathematics Theses

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