Students t-Distribution and Related Stochastic Processes [Paperback]

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-L?vy processes as Thorin subordinated Gaussian L?vy 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-L?vy 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-L?vy type processes, the notion of L?vy copulas and the related analogue of Sklars theorem are explained.Introduction.- Asymptotics.- Preliminaries of L?vy Processes.- Student-L?vy Processes.- Student OU-type Processes.- Student Diffusion Processes.- Miscellanea.- Bessel Functions.- References.- Index.

It is self-contained and summarizes the most recent results by the author related to t-distribution and their processes. & Grigelionis has pulled together an excellent overview in Student t-distribution and processes, which has not previously been available. The book is written at a highly scholarly level and should appeal to those with an interest in applied probability methodology and applications. It should be for students who have had an advanced course in probability. (Stergios B. Fotopoulos, Technometrics, Vol. 58 (3), August, 2016)

Prof. Grigelionis is a senior research fellow at the Institute of Mathematics and Informatics of Vilnius Univló