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Author Grigelionis, B. (Bronius), 1935-

Title Student's t-Distribution and related stochastic processes / Bronius Grigelionis
Published Heidelberg ; New York : Springer, [2013]
©2013
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Description 1 online resource (xi, 99 pages) : illustrations
Series SpringerBriefs in statistics, 2191-544X
SpringerBriefs in statistics.
Contents Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-Type Processes -- Student Diffusion Processes -- Miscellanea
Summary 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 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 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-Lévy type processes, the notion of Lévy copulas and the related analogue of Sklar's theorem are explained
Analysis Statistics
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Stochastic processes.
t-test (Statistics)
Form Electronic book
ISBN 3642311466 (electronic bk.)
9783642311468 (electronic bk.)