Student's t-Distribution and Related Stochastic Processes

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Beschreibung

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.



Autorentext

Prof. Grigelionis is a senior research fellow at the Institute of Mathematics and Informatics of Vilnius University, member of the Lithuanian Academy of Sciences and the International Statistical Institute. He has done extensive research in stochastic analysis and its applications. These include the semimartingale characterisation of stochastic processes with conditionally independent increments and solutions of stochastic Ito's equations, stochastic nonlinear filtering equations, optimal stopping of stochastic processes - joint research with A. Shiryaev - criteria of weak convergence of stochastic processes - joint research with R. Mikuleviius - etc. His current research topics are the properties of mixed Gaussian distributions and related stochastic processes.



Inhalt
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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Produktinformationen

Titel
Student's t-Distribution and Related Stochastic Processes
Autor
EAN
9783642311468
ISBN
978-3-642-31146-8
Format
E-Book (pdf)
Hersteller
Springer Berlin Heidelberg
Herausgeber
Springer
Genre
Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
Veröffentlichung
18.09.2012
Digitaler Kopierschutz
Adobe-DRM
Dateigrösse
1.39 MB
Anzahl Seiten
99
Jahr
2012
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