LEADER 03111nam 2200601 a 450 001 9910437866003321 005 20200520144314.0 010 $a1-283-63089-3 010 $a9786613943347 010 $a3-642-31146-6 024 7 $a10.1007/978-3-642-31146-8 035 $a(CKB)2670000000253996 035 $a(EBL)1030469 035 $a(OCoLC)811563993 035 $a(SSID)ssj0000767198 035 $a(PQKBManifestationID)11414662 035 $a(PQKBTitleCode)TC0000767198 035 $a(PQKBWorkID)10740098 035 $a(PQKB)11106821 035 $a(DE-He213)978-3-642-31146-8 035 $a(MiAaPQ)EBC1030469 035 $a(PPN)168318628 035 $a(EXLCZ)992670000000253996 100 $a20120801d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStudent's t-distribution and related stochastic processes /$fBronius Grigelionis 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (104 p.) 225 0$aSpringerBriefs in statistics,$x2191-544X 300 $aDescription based upon print version of record. 311 $a3-642-31145-8 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index. 330 $aThis brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Student?s distributions, represented as variance and mean-variance mixtures of multivariate Gaussian distributions with the reciprocal gamma mixing distribution. These results allow us to define and analyse Student-Lévy processes as Thorin subordinated Gaussian Lévy processes. A broad class of one-dimensional, strictly stationary diffusions with the Student?s t-marginal distribution are defined as the unique weak solution for the stochastic differential equation. Using the independently scattered random measures generated by the bi-variate centred Student-Lévy process, and stochastic integration theory, a univariate, strictly stationary process with the centred Student?s t- marginals and the arbitrary correlation structure are defined. As a promising direction for future work in constructing and analysing new multivariate Student-Lévy type processes, the notion of Lévy copulas and the related analogue of Sklar?s theorem are explained. 410 0$aSpringerBriefs in Statistics,$x2191-544X 606 $aStochastic processes 606 $aDistribution (Probability theory) 615 0$aStochastic processes. 615 0$aDistribution (Probability theory) 676 $a519.2 700 $aGrigelionis$b Bronius$0536470 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437866003321 996 $aStudent?s t-Distribution and Related Stochastic Processes$92539312 997 $aUNINA