Student's T-Distribution and Related Stochastic Processes
Grigelionis, Bronius
Student's T-Distribution and Related Stochastic Processes [electronic resource] - New York : Springer Sept. 2012 - SpringerBriefs in Statistics Ser. .
License restrictions may limit access.
Annotation This brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Students 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 Students 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 Students 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 Sklars theorem are explained.
Scholarly & Professional Springer
9783642311451 3642311458 (Trade Paper) USD 39.95 Retail Price (Publisher) = Student's T-Distribution and Related Stochastic Processes
9783642311451
3642311458 00024965
519.083 / GBS
Student's T-Distribution and Related Stochastic Processes [electronic resource] - New York : Springer Sept. 2012 - SpringerBriefs in Statistics Ser. .
License restrictions may limit access.
Annotation This brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Students 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 Students 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 Students 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 Sklars theorem are explained.
Scholarly & Professional Springer
9783642311451 3642311458 (Trade Paper) USD 39.95 Retail Price (Publisher) = Student's T-Distribution and Related Stochastic Processes
9783642311451
3642311458 00024965
519.083 / GBS