| 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 |
English |
|
Print version record |
| Subject |
Stochastic processes.
|
|
t-test (Statistics)
|
|
Stochastic Processes
|
|
MATHEMATICS -- Applied.
|
|
MATHEMATICS -- Probability & Statistics -- General.
|
|
Procesos estocásticos
|
|
Stochastic processes
|
|
t-test (Statistics)
|
|
t-Verteilung
|
|
Lévy-Prozess
|
|
Diffusionsprozess
|
| Form |
Electronic book
|
| ISBN |
9783642311468 |
|
3642311466 |
|
