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Grigelionis, Bronius - Student¿s t-Distribution and Related Stochastic Processes
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| Schrijver: | Grigelionis, Bronius |
| Titel: | Student¿s t-Distribution and Related Stochastic Processes |
| ISBN: | 9783642311451 |
| Uitgever: | Springer Berlin |
| Bijzonderheid: | 2012 112pp Paperback / softback |
| Prijs: |
€ 51,00
Gratis
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| Meer info | Annotatie 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 Flaptekst 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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