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003			BUT
005			20230525112805.0
006			m o d
007			cr|mn|---annan
008			202201s2021 x |||||o ||||eng|| d
020			_a9783039284580
020			_a9783039284597
040			_aoapen _coapen
041	0		_aeng
080			_a004
100	1		_aAvram, Florin _4edt
245	1	0	_aExit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics
260			_aBasel, Switzerland _bMDPI - Multidisciplinary Digital Publishing Institute _c2021
300			_a1 electronic resource (218 p.)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
506	0		_aOpen Access _2star _fUnrestricted online access
520			_aExit problems for one-dimensional Lévy processes are easier when jumps only occur in one direction. In the last few years, this intuition became more precise: we know now that a wide variety of identities for exit problems of spectrally-negative Lévy processes may be ergonomically expressed in terms of two q-harmonic functions (or scale functions or positive martingales) W and Z. The proofs typically require not much more than the strong Markov property, which hold, in principle, for the wider class of spectrally-negative strong Markov processes. This has been established already in particular cases, such as random walks, Markov additive processes, Lévy processes with omega-state-dependent killing, and certain Lévy processes with state dependent drift, and seems to be true for general strong Markov processes, subject to technical conditions. However, computing the functions W and Z is still an open problem outside the Lévy and diffusion classes, even for the simplest risk models with state-dependent parameters (say, Ornstein–Uhlenbeck or Feller branching diffusion with phase-type jumps).
540			_aCreative Commons _fhttps://creativecommons.org/licenses/by/4.0/ _2cc
546			_aEnglish
650		0	_aИнформационные технологии _94550
653			_aLévy processes
653			_anon-random overshoots
653			_askip-free random walks
653			_afluctuation theory
653			_ascale functions
653			_acapital surplus process
653			_adividend payment
653			_aoptimal control
653			_acapital injection constraint
653			_aspectrally negative Lévy processes
653			_areflected Lévy processes
653			_afirst passage
653			_adrawdown process
653			_aspectrally negative process
653			_adividends
653			_ade Finetti valuation objective
653			_avariational problem
653			_astochastic control
653			_aoptimal dividends
653			_aParisian ruin
653			_alog-convexity
653			_abarrier strategies
653			_aadjustment coefficient
653			_alogarithmic asymptotics
653			_aquadratic programming problem
653			_aruin probability
653			_atwo-dimensional Brownian motion
653			_aspectrally negative Lévy process
653			_ageneral tax structure
653			_afirst crossing time
653			_ajoint Laplace transform
653			_apotential measure
653			_aLaplace transform
653			_afirst hitting time
653			_adiffusion-type process
653			_arunning maximum and minimum processes
653			_aboundary-value problem
653			_anormal reflection
653			_aSparre Andersen model
653			_aheavy tails
653			_acompletely monotone distributions
653			_aerror bounds
653			_ahyperexponential distribution
653			_areflected Brownian motion
653			_alinear diffusions
653			_adrawdown
653			_aSegerdahl process
653			_aaffine coefficients
653			_aspectrally negative Markov process
653			_ahypergeometric functions
653			_acapital injections
653			_abankruptcy
653			_areflection and absorption
653			_aPollaczek–Khinchine formula
653			_ascale function
653			_aPadé approximations
653			_aLaguerre series
653			_aTricomi–Weeks Laplace inversion
700	1		_aAvram, Florin _4oth
856	4	0	_awww.oapen.org _uhttps://mdpi.com/books/pdfview/book/3954 _70 _zDownload
856	4	0	_awww.oapen.org _uhttps://directory.doabooks.org/handle/20.500.12854/76508 _70 _zDescription
909			_c255 _dRobiyakhon Olimjonova
942			_2udc _cEE
999			_c6644 _d6644