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Student's t-Distribution and Related Stochastic Processes
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....
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2013.
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| Edición: | 1st ed. 2013. |
| Colección: | SpringerBriefs in Statistics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 100 | 1 | |a Grigelionis, Bronius. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Student's t-Distribution and Related Stochastic Processes |h [electronic resource] / |c by Bronius Grigelionis. |
| 250 | |a 1st ed. 2013. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2013. | |
| 300 | |a XI, 99 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 505 | 0 | |a Introduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Statistics . | |
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| 830 | 0 | |a SpringerBriefs in Statistics, |x 2191-5458 | |
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