1.

Record Nr.

UNINA9910437866003321

Autore

Grigelionis Bronius

Titolo

Student's t-distribution and related stochastic processes / / Bronius Grigelionis

Pubbl/distr/stampa

New York, : Springer, 2013

ISBN

1-283-63089-3

9786613943347

3-642-31146-6

Edizione

[1st ed. 2013.]

Descrizione fisica

1 online resource (104 p.)

Collana

SpringerBriefs in statistics, , 2191-544X

Disciplina

519.2

Soggetti

Stochastic processes

Distribution (Probability theory)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Introduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index.

Sommario/riassunto

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.