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Field name	Details
Dewey Class	519.5
Title	Student's t-Distribution and Related Stochastic Processes ([Ebook]) / by Bronius Grigelionis.
Author	Grigelionis, Bronius
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer
Publication	, 2013.
Physical Details	XI, 99 pages : online resource.
Series	SpringerBriefs in Statistics 2191-544X
ISBN	9783642311468
Summary Note	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 Studentâs 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-Lévy process, and stochastic integration theory, a univariate, strictly stationary process with the centred Studentâs t- marginals and the arbitrary correlation structure are defined. As a promising direction for future work in constructing and analysing new multivariate Student-LÃ©vy type processes, the notion of Lévy copulas and the related analogue of Sklar's theorem are explained.:
Contents note	Introduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-642-31146-8
Links to Related Works	Subject References: Statistics . Statistics, general . Authors: Grigelionis, Bronius . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Statistics . Classification: 519.5 . 519.5 (DDC 23) .

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Student's t-Distribution and Related Stochastic Processes

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