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.

In-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Student's distributions

Extreme value theory for such diffusions is developed

Flexible and statistically tractable Kolmogorov-Pearson diffusions are described



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
9783642311451
ISBN
3642311458
Format
Kartonierter Einband
Herausgeber
Springer-Verlag GmbH
Genre
Mathematik
Anzahl Seiten
99
Gewicht
184g
Größe
H235mm x B155mm x T6mm
Jahr
2012
Untertitel
Englisch
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