Student's t-Distribution and Related Stochastic Processes

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Bronius Grigelionis, "Student's t-Distribution and Related Stochastic Processes "
English | ISBN: 3642311458 | 2013 | 112 pages | PDF | 1356 KB

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.

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