bokomslag Students t-Distribution and Related Stochastic Processes
Vetenskap & teknik

Students t-Distribution and Related Stochastic Processes

Bronius Grigelionis

Pocket

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  • 99 sidor
  • 2012
This brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Students 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-Lvy processes as Thorin subordinated Gaussian Lvy processes. A broad class of one-dimensional, strictly stationary diffusions with the Students 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-Lvy process, and stochastic integration theory, a univariate, strictly stationary process with the centred Students t- marginals and the arbitrary correlation structure are defined. As a promising direction for future work in constructing and analysing new multivariate Student-Lvy type processes, the notion of Lvy copulas and the related analogue of Sklars theorem are explained.
  • Författare: Bronius Grigelionis
  • Format: Pocket/Paperback
  • ISBN: 9783642311451
  • Språk: Engelska
  • Antal sidor: 99
  • Utgivningsdatum: 2012-09-18
  • Förlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K