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Record Nr. |
UNINA9910437866003321 |
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Autore |
Grigelionis Bronius |
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Titolo |
Student's t-distribution and related stochastic processes / / Bronius Grigelionis |
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Pubbl/distr/stampa |
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New York, : Springer, 2013 |
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ISBN |
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1-283-63089-3 |
9786613943347 |
3-642-31146-6 |
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Edizione |
[1st ed. 2013.] |
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Descrizione fisica |
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1 online resource (104 p.) |
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Collana |
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SpringerBriefs in statistics, , 2191-544X |
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Disciplina |
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Soggetti |
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Stochastic processes |
Distribution (Probability theory) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Introduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index. |
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Sommario/riassunto |
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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. |
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