Moments and polynomial expansions in discrete matrix-analytic models
Tài liệu tham khảo
Aldous, 1987, The least variable phase type distribution is Erlang, Commun. Stat. Stoch. Model., 3, 467, 10.1080/15326348708807067
Arley, 1945, On the theory of infinite systems of differential equations and their application to the theory of stochastic processes and the perturbation theory of quantum mechanics, Acta Math., 76, 261, 10.1007/BF02551579
Asmussen, 2003
Asmussen, 2002, Erlangian approximations for finite-horizon ruin probabilities, Astin Bull., 32, 267, 10.2143/AST.32.2.1029
Asmussen, 2007
Asmussen, 2018, A factorization of a Lévy process over a phase-type horizon, Stoch. Models, 34, 397, 10.1080/15326349.2018.1513335
Asmussen, 1993, Marked point processes as limits of Markovian arrival streams, J. Appl. Probab., 30, 365, 10.2307/3214845
Asmussen, 2019, Phase-type models in life insurance: Fitting and valuation of equity-linked benefits, Risks, 7, 17, 10.3390/risks7010017
Bini, 2005
Bladt, 2020, Matrix representations of life insurance payments, Eur. Actuar. J., 10.1007/s13385-019-00222-0
Bladt, 2017
Bladt, 2019, Parisian types of ruin probabilities for a class of dependent risk-reserve processes, Scand. Actuar. J., 2019, 32, 10.1080/03461238.2018.1483420
Carr, 1998, Randomization and the American put, Rev. Financ. Stud., 11, 597, 10.1093/rfs/11.3.597
Cohen, 1982
Cramér, 1946
van Dijk, 2018, Uniformization: Basics, extensions and applications, Perform. Eval., 118, 8, 10.1016/j.peva.2017.09.008
Gill, 1990, A survey of product-integration with a view toward application in survival analysis, Ann. Statist., 18, 1501, 10.1214/aos/1176347865
Hald, 2000, The early history of the cumulants and the Gram-Charlier series, Int. Stat. Rev., 68, 137, 10.1111/j.1751-5823.2000.tb00318.x
Helton, 1976, Numerical approximation of product integrals, J. Math. Anal. Appl., 56, 410, 10.1016/0022-247X(76)90053-6
Koekoek, 1996
Latouche, 1999
Meixner, 1934, Orthogonale Polynomsysteme mit einer Besonderen Gestalt der Erzeugenden Funktion, J. Lond. Math. Soc., s1-9, 6, 10.1112/jlms/s1-9.1.6
Moler, 2003, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45, 1, 10.1137/S00361445024180
Møller, 1992, Numerical evaluation of Markov transition probabilities based on the discretized product integral, Scand. Actuar. J., 1992, 76, 10.1080/03461238.1992.10413898
Narayana, 1992, The first two moment matrices of the counts for the Markovian arrival process, Commun. Stat. Stoch. Model., 8, 459, 10.1080/15326349208807234
Neuts, 1981
Nielsen, 2007, Higher order moments and conditional asymptotics of the batch Markovian arrival process, Stoch. Models, 23, 1, 10.1080/15326340601141844
O’Cinneide, 1991, Phase-type distributions and majorization, Ann. Appl. Probab., 1, 219
Rolski, 2009
Szegö, 1959
Van Loan, 1978, Computing integrals involving the matrix exponential, IEEE Trans. Automat. Control, 23, 395, 10.1109/TAC.1978.1101743
Whitt, 2014, Heavy-traffic limits for queues with periodic arrival processes, Oper. Res. Lett., 42, 458, 10.1016/j.orl.2014.08.001
Withers, 2009, Charlier and edgeworth expansions for distributions and densities in terms of bell polynomials, Probab. Math. Statist., 29, 271
