Student's t-distribution and related stochastic processes
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Bibliographic Information
Student's t-distribution and related stochastic processes
（Springer Briefs in statistics）
Springer, c2013
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Includes bibliographical references and index
Description and Table of Contents
Description
This brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Student's distributions, represented as variance and mean-variance mixtures of multivariate Gaussian distributions with the reciprocal gamma mixing distribution. These results allow us to define and analyse Student-Levy processes as Thorin subordinated Gaussian Levy processes. A broad class of one-dimensional, strictly stationary diffusions with the Student's t-marginal distribution are defined as the unique weak solution for the stochastic differential equation. Using the independently scattered random measures generated by the bi-variate centred Student-Levy process, and stochastic integration theory, a univariate, strictly stationary process with the centred Student's t- marginals and the arbitrary correlation structure are defined. As a promising direction for future work in constructing and analysing new multivariate Student-Levy type processes, the notion of Levy copulas and the related analogue of Sklar's theorem are explained.
Table of Contents
Introduction.- Asymptotics.- Preliminaries of Levy Processes.- Student-Levy Processes.- Student OU-type Processes.- Student Diffusion Processes.- Miscellanea.- Bessel Functions.- References.- Index.
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