EAN: 9783642311451

SPRINGERBRIEFS IN STATISTICS STUDENTS T-DISTR...

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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