Student’s t-Distribution and Related Stochastic Processes

  • Bronius Grigelionis

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Bronius Grigelionis
    Pages 1-7
  3. Bronius Grigelionis
    Pages 9-20
  4. Bronius Grigelionis
    Pages 21-40
  5. Bronius Grigelionis
    Pages 41-50
  6. Bronius Grigelionis
    Pages 51-56
  7. Bronius Grigelionis
    Pages 57-76
  8. Bronius Grigelionis
    Pages 77-91
  9. Back Matter
    Pages 93-99

About this book

Introduction

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.

Keywords

Bessel function Gaussian Lévy process H-diffusion Self-decomposability Thorin subordinator

Authors and affiliations

  • Bronius Grigelionis
    • 1
  1. 1.University of VilniusVilniusLithuania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-31146-8
  • Copyright Information The Author(s) 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-31145-1
  • Online ISBN 978-3-642-31146-8
  • Series Print ISSN 2191-544X
  • Series Online ISSN 2191-5458
  • About this book
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