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Student’s t-Distribution and Related Stochastic Processes

Produktform: E-Buch Text Elektronisches Buch in proprietärem

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-Lévy processes as Thorin subordinated Gaussian Lévy processes. A broad class of one-dimensional, strictly stationary diffusions with the Student’s -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-Lévy process, and stochastic integration theory, a univariate, strictly stationary process with the centred Student’s marginals and the arbitrary correlation structure are defined. As a promising direction for future work in constructing and analysing new multivariate Student-Lévy type processes, the notion of Lévy copulas and the related analogue of Sklar’s theorem are explained.weiterlesen

Dieser Artikel gehört zu den folgenden Serien

Elektronisches Format: PDF

Sprache(n): Englisch

ISBN: 978-3-642-31146-8 / 978-3642311468 / 9783642311468

Verlag: Springer Berlin

Erscheinungsdatum: 18.09.2012

Seiten: 99

Autor(en): Bronius Grigelionis

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