Skip to main content Accessibility help
×
×
Home

The intersite distances between pattern occurrences in strings generated by general discrete- and continuous-time models: an algorithmic approach

  • Valeri T. Stefanov (a1)

Abstract

The formation of patterns from letters of a finite alphabet is considered. The strings of letters are generated by general discrete- and continuous-time models which embrace as particular cases all models considered in the literature. The letters of the alphabet are identified by the states of either discrete- or continuous-time semi-Markov processes. A new and unifying method is introduced for evaluation of the generating functions of both the intersite distance between occurrences of an arbitrary, but fixed, pattern and the waiting time until the first occurrence of that pattern. Our method also covers in a unified way relevant and important joint generating functions. Furthermore, our results lead to an easy and efficient implementation of the relevant evaluations.

Copyright

Corresponding author

Postal address: School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia. Email address: stefanov@maths.uwa.edu.au

References

Hide All
Antzoulakos, D. L. (2001). Waiting times for patterns in a sequence of multistate trials. J. Appl. Prob. 38, 508518.
Balakrishnan, N., and Koutras, M. (2002). Runs and Scans with Applications. John Wiley, New York.
Biggins, J. D. (1987). A note on repeated sequences in Markov chains. Adv. Appl. Prob. 19, 739742.
Biggins, J. D., and Cannings, C. (1987). Markov renewal processes, counters and repeated sequences in Markov chains. Adv. Appl. Prob. 19, 521545.
Blom, G., and Thorburn, D. (1982). How many random digits are required until given sequences are obtained? J. Appl. Prob. 19, 518531.
Chadjiconstantinidis, S., Antzoulakos, D. L., and Koutras, M. V. (2000). Joint distributions of successes, failures and patterns in enumeration problems. Adv. Appl. Prob. 32, 866884.
Chryssaphinou, O., and Papastavridis, S. (1990). The occurrence of a sequence of patterns in repeated dependent experiments. Theory Prob. Appl. 35, 167173.
Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.
Feller, W. (1950). An Introduction to Probability Theory and Its Applications, Vol. 1. John Wiley, New York.
Fu, J. C. (1996). Distribution theory of runs and patterns associated with a sequence of multistate trials. Statistica Sinica 6, 957974.
Fu, J. C., and Chang, Y. M. (2002). On probability generating functions for waiting time distributions of compound patterns in a sequence of multistate trials. J. Appl. Prob. 39, 7080.
Gerber, H. and Li, S.-Y. R. (1981). The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain. Stoch. Process. Appl. 11, 101108.
Guibas, L. J., and Odlyzko, A. M. (1981). String overlaps, pattern matching, and nontransitive games. J. Combinatorial Theory A 30, 183208.
Kijima, M. (1997). Markov Processes for Stochastic Modelling. Chapman and Hall, London.
Li, S.-Y. R. (1980). A martingale approach to the study of occurrence of sequence patterns in repeated experiments. Ann. Prob. 8, 11711176.
Reinert, G., Schbath, S., and Waterman, M. (2000). Probabilistic and statistical properties of words: an overview. J. Comput. Biol. 7, 146.
Robin, S., and Daudin, J. (1999). Exact distribution of word occurrences in a random sequence of letters. J. Appl. Prob. 36, 179193.
Stefanov, V. T. (2000). On some waiting time problems. J. Appl. Prob. 37, 756764.
Stefanov, V. T., and Pakes, A. G. (1997). Explicit distributional results in pattern formation. Ann. Appl. Prob. 7, 666678.
Syski, R. (1992). Passage Times for Markov Chains. IOS Press, Amsterdam.
Szpankowski, W. (2001). Average Case Analysis of Algorithms on Sequences. John Wiley, New York.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed