The asymptotics of waiting times between stationary processes, allowing distortion

Annals of Applied Probability

Volumn 9, Issue 2, 1999, Pages 413-429

  Dembo, Amir ^a   Kontoyiannis, Ioannis ^b  

^a STANFORD UNIVERSITY   (United States)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Almost sure invariance principle; Large deviations; Relative entropy; String matching; Strong approximation; Waiting times

Indexed keywords

EID: 0033437915     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1029962749     Document Type: Article

References (22)

1. ARRATIA, R. and WATERMAN, M. S. (1994). A phase transition for the score in matching random sequences allowing deletions. Ann. Appl. Probab. 4 200-225.
2. BERGER, T. (1971). Rate Distortion Theory. Prentice-Hall, Englewood Cliffs, NJ.
3. BRADLEY, B. C. (1986). Basic properties of strong mixing conditions. In Progress in Probability and Statistics 11 (E. Eberlein and M. S. Taqqu, eds.) 165-192. Birkhauser, Boston.
4. DEUSCHEL, J. D. and STROOCK, D. W. (1989). Large Deviations. Academic Press, Boston.
5. IBRAGIMOV, I. A. (1962). Some limit theorems for stationary processes. Theory Probab. Appl. 7 349-382.
6. KARLIN, S. and OST, F. (1988). Maximal length of common words among random letter sequences. Ann. Probab. 16 535-563.
7. KONTOYIANNIS, I. (1998). Asymptotic recurrence and waiting times for stationary processes. J. Theoret. Probab. 11 795-811.
8. ŁUCZAK, T. and SZPANKOWSKI, W. (1997). A suboptimal lossy data compression based on approximate pattern matching. IEEE Trans. Inform. Theory 43 1439-1451.
9. MARTON, K. and SHIELDS, P. C. (1995). Almost-sure waiting time results for weak and very weak Bernoulli processes. Ergodic Theory Dynam. Systems 15 951-960.
10. PELIGRAD, M. (1986). Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables (a survey). In Progress in Probability and Statistics 11 (E. Eberlein and M. S. Taqqu, eds.) 193-223. Birkhauser, Boston.
11. PEVZNER, P., BORODOVSKY, M. and MIRONOV, A. (1991). Linguistic of nucleotide sequences: the significance of deviations from mean statistical characteristics and prediction of the frequency of occurrence of words. J. Biomol. Struct. Dynam. 6 1013-1026.
12. PHILIPP, W. and STOUT, W. (1975). Almost Sure Invariance Principles for Partial Sums of Weakly Dependent Random Variables. Mem. Amer. Soc. 2 Amer. Math. Soc., Providence, RI.
13. RAO, R. R. (1962). Relations between weak and uniform convergence of measures with applications. Ann. Math. Statist. 33 659-680.
14. RIO, E. (1995). The functional law of the iterated logarithm for stationary strongly mixing sequences. Ann. Probab. 23 1188-1203.
15. SHIELDS, P. C. (1993). Waiting times: positive and negative results on the Wyner-Ziv problem. J. Theoret. Probab. 6 499-519.
16. STEINBERG, Y. and GUTMAN, M. (1993). An algorithm for source coding subject to a fidelity criterion based on string matching. IEEE Trans. Inform. Theory 39 877-886.
17. STRASSEN, V. (1964). An almost sure invariance principle for the law of the iterated logarithm. Z. Wahrsch. Verw. Gebiete 3 23-32.
18. SZPANKOWSKI, W. (1993). Asymptotic properties of data compression and suffix trees. IEEE Trans. Inform. Theory 39 1647-1659.
19. WYNER, A. J. (1993). String matching theorems and applications to data compression and statistics. Ph.D. dissertation, Dept. Statistics, Stanford Univ.
20. WYNER, A. D. and ZIV, J. (1989). Some asymptotic properties of the entropy of a stationary ergodic data source with applications to data compression. IEEE Trans. Inform. Theory 35 1250-1258.
21. WYNER, A. D. and ZIV, J. (1991). Fixed data base version of the Lempel-Ziv data compression algorithm. IEEE Trans. Inform. Theory 37 878-880.
22. YANG, E.-H. and KIEFFER, J. C. (1998). On the performances of data compression algorithms based upon string matching. IEEE Trans. Inform. Theory 44 47-65.