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008 170212s2015 gw | s |||| 0|eng d
020 _a9783319231389
_9978-3-319-23138-9
024 7 _a10.1007/978-3-319-23138-9
_2doi
035 _ato000560710
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aAndersen, Lars Nørvang.
_eauthor.
_9467688
245 1 0 _aLévy Matters V
_helectronic 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.
260 _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
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_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 _amathematics.
_9566183
650 0 _aProbabilities.
_9295556
650 1 4 _aMathematics.
_9566184
650 2 4 _aProbability Theory and Stochastic Processes.
_9303734
700 1 _aAsmussen, Søren.
_eauthor.
_9306718
700 1 _aAurzada, Frank.
_eauthor.
_9467689
700 1 _aGlynn, Peter W.
_eauthor.
_9306719
700 1 _aMaejima, Makoto.
_eauthor.
_9467690
700 1 _aPihlsgård, Mats.
_eauthor.
_9467691
700 1 _aSimon, Thomas.
_eauthor.
_9467692
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
830 0 _aLecture Notes in Mathematics,
_9315276
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-23138-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c415319