EAN: 9783642311451

Bilder-Quelle: discount24.de - Sport-Freizeit

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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12.05.2025 um 14:49 Uhr

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