{"product_id":"students-t-distribution-and-related-stochastic-processes-9783642311451","title":"Student's T-Distribution and Related Stochastic Processes","description":"\u003cp\u003e • Author(s): Bronius Grigelionis\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Probability \u0026amp; Statistics - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003eThis 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 \u003ci\u003et\u003c\/i\u003e-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 \u003ci\u003et-\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45279637209239,"sku":"9783642311451","price":2935.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783642311451.webp?v=1769294131","url":"https:\/\/atlanticbooks.com\/products\/students-t-distribution-and-related-stochastic-processes-9783642311451","provider":"Atlantic Books","version":"1.0","type":"link"}