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020 _a9783642311468
_9978-3-642-31146-8
024 7 _a10.1007/978-3-642-31146-8
_2doi
050 4 _aQA276-280
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.5
_223
100 1 _aGrigelionis, Bronius.
_eauthor.
245 1 0 _aStudent’s t-Distribution and Related Stochastic Processes
_h[electronic resource] /
_cby Bronius Grigelionis.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXI, 99 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Statistics,
_x2191-544X
505 0 _aIntroduction -- Asymptotics -- Preliminaries of Lévy Processes -- Student-Lévy Processes -- Student OU-type Processes -- Student Diffusion Processes -- Miscellanea -- Bessel Functions -- References -- Index.
520 _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.
650 0 _aStatistics.
650 1 4 _aStatistics.
650 2 4 _aStatistics, general.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642311451
830 0 _aSpringerBriefs in Statistics,
_x2191-544X
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-31146-8
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c46003
_d46003