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020 _a9783319231389
_9978-3-319-23138-9
024 7 _a10.1007/978-3-319-23138-9
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aAndersen, Lars Nørvang.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLévy Matters V
_h[electronic resource] :
_bFunctionals of Lévy Processes /
_cby Lars Nørvang Andersen, Søren Asmussen, Frank Aurzada, Peter W. Glynn, Makoto Maejima, Mats Pihlsgård, Thomas Simon.
250 _a1st ed. 2015.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXVI, 224 p. 8 illus., 7 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLévy Matters, A Subseries on Lévy Processes,
_x2190-6637 ;
_v2149
505 0 _aMakoto Maejima: Classes of infinitely divisible distributions and examples -- Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgard: Lévy processes with two-sided reflection -- Persistence probabilities and exponents -- Frank Aurzada and Thomas Simon: Persistence probabilities and exponents.
520 _aThis three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier.  If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process.  .
650 0 _aDistribution (Probability theory.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
700 1 _aAsmussen, Søren.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aAurzada, Frank.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aGlynn, Peter W.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aMaejima, Makoto.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aPihlsgård, Mats.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSimon, Thomas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319231372
776 0 8 _iPrinted edition:
_z9783319231396
830 0 _aLévy Matters, A Subseries on Lévy Processes,
_x2190-6637 ;
_v2149
856 4 0 _uhttps://doi.org/10.1007/978-3-319-23138-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9695
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