Logarithmic asymptotics for the supremum of a stochastic process

Annals of Applied Probability

Volumn 13, Issue 2, 2003, Pages 430-445

  Duffy, Ken ^a   Lewis, John T ^a   Sullivan, Wayne G ^a  

^a DUBLIN INSTITUTE OF TECHNOLOGY   (Ireland)

Author keywords

Extrema of stochastic process; Large deviation theory; Queueing theory

Indexed keywords

EID: 21144442194     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/aoap/1050689587     Document Type: Article

References (14)

1. ASMUSSEN, S. and COLLAMORE, J. F. (1999). Exact asymptotics for a large deviations problem for the GI/G/1 queue. Markov Process. Related Fields 5 451-476.
2. BINGHAM, N. H., GOLDIE, C. M. and TEUGELS, J. L. (1987). Regular Variation. Cambridge Univ. Press.
3. DEMBO, A. and ZEITOUNI, O. (1998). Large Deviation Techniques and Applications. Springer, Berlin.
4. DUFFIELD, N. G. and O'CONNELL, N. (1995). Large deviations and overflow probabilities for the general single server queue, with applications. Math. Proc. Cambridge Philos. Soc. 118 363-374.
5. DUFFY, K. (2000). Logarithmic asymptotics in queueing theory and risk theory. Ph.D. thesis, Trinity College, Dublin.
6. ELLIS, R. (1984). Large deviations for a general class of random vectors. Ann. Probab. 12 1-12.
7. GÄRTNER, J. (1977). On large deviations from the invariant measure. Theory Probab. Appl. 22 24-39.
8. GLYNN, P. and WHITT, W. (1994). Logarithmic asymptotics for steady-state tail probabilities in a single-server queue. J. Appl. Probab. 31A 413-430.
9. HALMOS, P. R. (1956). Ergodic Theory. Chelesa, New York.
10. LIU, Z., NAIN, P., TOWSLEY, D. and ZHANG, Z. L. (1999). Asymptotic behavior of a multiplexer fed with a long-range dependent process. J. Appl. Probab. 36 105-118.
11. LOYNES, R. M. (1962). The stability of a queue with non-independent inter-arrival and service times. Proc. Cambridge Philos. Soc. 58 497-520.
12. MASSOULIE, L. and SIMONIAN, A. (1999). Large buffer asymptotics for the queue fed with FBM input. J. Appl. Probab. 36 894-906.
13. MIKOSCH, T. and NAGAEV, A. V. (1998). Large deviations of heavy-tailed sums with applications in insurance. Extremes 1 81-110.
14. PARULEKAR, M. and MAKOWSKI, A. M. (1997). M/G/∞ input processes: A versatile class of models for network traffic. IEEE INFOCOM 2 419-426.