Sample-Path Large Deviations for Unbounded Additive Functionals of the Reflected Random Walk

Published Online:https://doi.org/10.1287/moor.2020.0094

References

  • [1] Bazhba M, Blanchet J, Laeven RJA, Zwart B (2022) Large deviations asymptotics for unbounded additive functionals of diffusion processes. Preprint, submitted February 22, https://arxiv.org/abs/2202.10799.Google Scholar
  • [2] Bazhba M, Blanchet J, Rhee CH, Zwart B (2019) Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times. Queueing Systems 93(3–4):195–226.CrossrefGoogle Scholar
  • [3] Bazhba M, Blanchet J, Rhee CH, Zwart B (2020) Sample path large deviations for Lévy processes and random walks with Weibull increments. Ann. Appl. Probab. 30(6):2695–2739.CrossrefGoogle Scholar
  • [4] Blanchet J, Glynn P, Meyn S (2013) Large deviations for the empirical mean of an M/M/1 queue. Queueing Systems 73(4):425–446.CrossrefGoogle Scholar
  • [5] Borovkov AA, Mogulskii AA (2013) Large deviation principles for random walk trajectories. II. Theory Probab. Appl. 57(1):1–27.CrossrefGoogle Scholar
  • [6] Borovkov AA, Mogulskii AA (2014) Large deviation principles for random walk trajectories. III. Theory Probab. Appl. 58(1):25–37.CrossrefGoogle Scholar
  • [7] Cesari L (1983) Problems with ordinary differential equations. Optimization—Theory and Applications, Applications of Mathematics, vol. 17 (Springer-Verlag, New York).Google Scholar
  • [8] Dembo A, Zeitouni O (2010) Large Deviations Techniques and Applications. Stochastic Modelling and Applied Probability, vol. 38 (Springer-Verlag, Berlin).CrossrefGoogle Scholar
  • [9] Donsker M, Varadhan S (1975) Asymptotic evaluation of certain Markov process expectations for large time, II. Comm. Pure Appl. Math. 28(2):279–301.CrossrefGoogle Scholar
  • [10] Duffy KR, Meyn SP (2014) Large deviation asymptotics for busy periods. Stochastic Systems 4(1):300–319.LinkGoogle Scholar
  • [11] Ganesh A, O’Connell N, Wischik D (2004) Big Queues. Lecture Notes in Mathematics, vol. 1838 (Springer-Verlag, Berlin).CrossrefGoogle Scholar
  • [12] Gantert N (1998) Functional Erdos-Renyi laws for semiexponential random variables. Ann. Probab. 26(3):1356–1369.CrossrefGoogle Scholar
  • [13] Kontoyiannis I, Meyn SP (2003) Spectral theory and limit theorems for geometrically ergodic Markov processes. Ann. Appl. Probab. 13(1):304–362.CrossrefGoogle Scholar
  • [14] Lynch J, Sethuraman J (1987) Large deviations for processes with independent increments. Ann. Probab. 15(2):610–627.CrossrefGoogle Scholar
  • [15] Mogulskii AA (1993) Large deviations for processes with independent increments. Ann. Probab. 21(1):202–215.CrossrefGoogle Scholar
  • [16] Nuyens M, Zwart B (2006) A large-deviations analysis of the GI/GI/1 SRPT queue. Queueing Systems 54(2):85–97.CrossrefGoogle Scholar
  • [17] Puhalskii AA, Whitt W (1997) Functional large deviation principles for first-passage-time processes. Ann. Appl. Probab. 7(2):362–381.CrossrefGoogle Scholar
  • [18] Puhalskii AA, Whitt W (1998) Functional large deviation principles for waiting and departure processes. Probab. Engrg. Inform. Sci. 12(4):479–507.CrossrefGoogle Scholar
  • [19] Ramasubramanian S (2000) A subsidy-surplus model and the Skorokhod problem in an orthant. Math. Oper. Res. 25(3):509–538.LinkGoogle Scholar
  • [20] Sforzo R (2005) Reversible Markov processes on general spaces and spatial migration processes. Adv. Appl. Probab. 37(3):801–818.CrossrefGoogle Scholar
  • [21] Vysotsky V (2021) Contraction principle for trajectories of random walks and Cramér’s theorem for kernel-weighted sums. ALEA Latin Amer. J. Probab. Math. Statist. 18(2):1103–1125.CrossrefGoogle Scholar
  • [22] Whitt W (2002) Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues (Springer Science & Business Media, New York).CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.