TY  - BOOK
AU  - Grigelionis,Bronius
TI  - Student's T-Distribution and Related Stochastic Processes
SN  - 9783642311451
U1  - 519.083 22
PY  - 2012///
CY  - New York : 
PB  - Springer
N1  - License restrictions may limit access; Scholarly & Professional; Springer
N2  - 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
UR  - http://www.columbia.edu/cgi-bin/cul/resolve?clio10192925
ER  -