Student’s t-Distribution and Related Stochastic Processes
Grigelionis, Bronius.
Student’s t-Distribution and Related Stochastic Processes [electronic resource] / by Bronius Grigelionis. - XI, 99 p. online resource. - SpringerBriefs in Statistics, 2191-544X . - SpringerBriefs in Statistics, .
Introduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index.
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.
9783642311468
10.1007/978-3-642-31146-8 doi
Statistics.
Statistics.
Statistics, general.
QA276-280
519.5
Student’s t-Distribution and Related Stochastic Processes [electronic resource] / by Bronius Grigelionis. - XI, 99 p. online resource. - SpringerBriefs in Statistics, 2191-544X . - SpringerBriefs in Statistics, .
Introduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index.
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.
9783642311468
10.1007/978-3-642-31146-8 doi
Statistics.
Statistics.
Statistics, general.
QA276-280
519.5