Format:
Online-Ressource (XI, 99 p, digital)
ISBN:
9783642311468
Series Statement:
SpringerBriefs in Statistics
Content:
Introduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index.
Content:
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.
Additional Edition:
ISBN 9783642311451
Additional Edition:
Buchausg. u.d.T. Grigelionis, Bronius, 1935 - 2014 Student's t-distribution and related stochastic processes Heidelberg [u.a.] : Springer, 2013 ISBN 9783642311451
Additional Edition:
ISBN 3642311458
Language:
English
Subjects:
Mathematics
Keywords:
t-Verteilung
;
Lévy-Prozess
;
Diffusionsprozess
DOI:
10.1007/978-3-642-31146-8
URL:
Volltext
(lizenzpflichtig)
