Extreme Value Analysis for a Markov Additive Process Driven by a Nonirreducible Background Chain

Published Online:https://doi.org/10.1287/stsy.2021.0086

References

  • Abate J, Whitt W (2006) A unified framework for numerically inverting Laplace transforms. INFORMS J. Comput. 18(4):408–421.LinkGoogle Scholar
  • Asmussen S (2003) Applied Probability and Queues, 2nd ed. (Springer, New York).Google Scholar
  • Asmussen S, Ivanovs J (2018) A factorization of a Lévy process over a phase-type horizon. Stochastic Models 34(4):397–408.Google Scholar
  • Asmussen S, Kella O (2000) A multi-dimensional martingale for Markov additive processes and its applications. Adv. Appl. Probab. 32(2):376–393.Google Scholar
  • Boxma O, Mandjes M (2021) Affine storage and insurance risk models. Math. Oper. Res. 46(4):1282–1302.Google Scholar
  • Çinlar E (1972) Markov additive processes I. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 24:85–93.Google Scholar
  • D’Auria B, Ivanovs J, Kella O, Mandjes M (2010) First passage of a Markov additive process and generalized Jordan chains. J. Appl. Probab. 47(4):1048–1057.Google Scholar
  • Dȩbicki K, Mandjes M (2015) Queues and Lévy Fluctuation Theory (Springer, New York).Google Scholar
  • Delsing G, Mandjes M (2021) A transient Cramér-Lundberg model with applications to credit risk. J. Appl. Probab. 58(3):721–745. Google Scholar
  • Dieker A, Mandjes M (2011) Extremes of Markov-additive processes with one-sided jumps, with queueing applications. Methodology Comput. Appl. Probab. 13:221–267.Google Scholar
  • Ivanovs J (2011) One-sided Markov additive processes and related exit problems. Unpublished PhD thesis, University of Amsterdam, Netherlands.Google Scholar
  • Ivanovs J (2017) Splitting and time reversal for Markov additive processes. Stochastic Processes Their Appl. 127(8):2699–2724.Google Scholar
  • Ivanovs J, Boxma O, Mandjes M (2010) Singularities of the matrix exponent of a Markov additive process with one-sided jumps. Stochastic Processes Their Appl. 120(9):1776–1794.Google Scholar
  • Kyprianou A (2006) Introductory Lectures on Fluctuations of Lévy Processes with Applications (Springer, New York).Google Scholar
  • Lewis A, Mordecki E (2008) Wiener-Hopf factorization for Lévy processes having positive jumps with rational transforms. J. Appl. Probab. 45(1):118–134.Google Scholar
  • Neveu J (1961) Une généralisation des processus à accroissements positifs indépendents. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 25:36–61.Google Scholar
  • Starreveld N, Bekker R, Mandjes M (2016) Transient analysis of one-sided Lévy-driven queues. Stochastic Models 32(3):481–512.Google Scholar
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