Free Access
Issue
ESAIM: PS
Volume 14, 2010
Page(s) 435 - 455
DOI https://doi.org/10.1051/ps/2009008
Published online 22 December 2010
  1. C. Andriani and P. Baldi, Sharp estimates of deviations of the sample mean in many dimensions. Ann. Inst. H. Poincaré Probab. Statist. 33 (1997) 371–385. [CrossRef] [MathSciNet] [Google Scholar]
  2. R.R. Bahadur and R.R. Rao, On deviations of the sample mean. Ann. Math. Statist. 31 (1960) 1015–1027. [CrossRef] [MathSciNet] [Google Scholar]
  3. P. Barbe and M. Broniatowski, Large-deviation probability and the local dimension of sets, in Proceedings of the 19th Seminar on Stability Problems for Stochastic Models, Vologda, 1998, Part I. (2000), Vol. 99, pp. 1225–1233. [Google Scholar]
  4. N.R. Chaganty and J. Sethuraman, Strong large deviation and local limit theorems. Ann. Probab. 21 (1993) 1671–1690. [CrossRef] [MathSciNet] [Google Scholar]
  5. S. Datta and W.P. McCormick, On the first-order Edgeworth expansion for a Markov chain. J. Multivariate Anal. 44 (1993) 345–359. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Dembo and O. Zeitouni, Large deviations techniques and applications. Volume 38 of Appl. Math. (New York). Second edition. Springer-Verlag, New York (1998). [Google Scholar]
  7. P. Flajolet, W. Szpankowski and B. Vallée, Hidden word statistics. J. ACM 53 (2006) 147–183 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Iltis, Sharp asymptotics of large deviations in Rd. J. Theoret. Probab. 8 (1995) 501–522. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Iltis, Sharp asymptotics of large deviations for general state-space Markov-additive chains in Rd. Statist. Probab. Lett. 47 (2000) 365–380. [CrossRef] [MathSciNet] [Google Scholar]
  10. I. Iscoe, P. Ney and E. Nummelin, Large deviations of uniformly recurrent Markov additive processes. Adv. Appl. Math. 6 (1985) 373–412. [CrossRef] [MathSciNet] [Google Scholar]
  11. J.L. Jensen, Saddlepoint approximations. The Clarendon Press Oxford University Press, New York (1995). [Google Scholar]
  12. V. Kargin, A large deviation inequality for vector functions on finite reversible Markov chains. Ann. Appl. Probab. 17 (2007) 1202–1221. [CrossRef] [MathSciNet] [Google Scholar]
  13. K. Knopp, Theory of Functions, Part I. Elements of the General Theory of Analytic Functions. Dover Publications, New York (1945). [Google Scholar]
  14. I. Kontoyiannis and S.P. Meyn, Spectral theory and limit theorems for geometrically ergodic Markov processes. Ann. Appl. Probab. 13 (2003) 304–362. [CrossRef] [MathSciNet] [Google Scholar]
  15. C.A. León and F. Perron, Optimal Hoeffding bounds for discrete reversible Markov chains. Ann. Appl. Probab. 14 (2004) 958–970. [CrossRef] [MathSciNet] [Google Scholar]
  16. M.E. Lladser, M.D. Betterton and R. Knight, Multiple pattern matching: a Markov chain approach. J. Math. Biol. 56 (2008) 51–92. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  17. B. Mann, Berry-Esseen Central Limit Theorems For Markov Chains. Ph.D. thesis, Harvard University, 1996. [Google Scholar]
  18. H.D. Miller, A convexivity property in the theory of random variables defined on a finite Markov chain. Ann. Math. Statist. 32 (1961) 1260–1270. [CrossRef] [MathSciNet] [Google Scholar]
  19. P. Ney, Dominating points and the asymptotics of large deviations for random walk on Rd. Ann. Probab. 11 (1983) 158–167. [CrossRef] [MathSciNet] [Google Scholar]
  20. P. Ney and E. Nummelin, Markov additive processes, Part I. Eigenvalue properties and limit theorems. Ann. Probab. 15 (1987) 561–592. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Nicodème, B. Salvy and P. Flajolet, Motif statistics. In Algorithms – ESA '99, Prague. Lect. Notes Comput. Sci. 1643. Springer, Berlin (1999), pp 194–211. [Google Scholar]
  22. G. Nuel, Numerical solutins for Patterns Statistics on Markov chains. Stat. Appl. Genet. Mol. Biol. 5 (2006). [Google Scholar]
  23. G. Nuel, Pattern Markov chains: optimal Markov chain embedding through deterministic finite automata. J. Appl. Probab. 45 (2008) 226–243. [CrossRef] [MathSciNet] [Google Scholar]
  24. R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2003). ISBN 3-900051-00-3. [Google Scholar]
  25. M. Régnier, A unified approach to word occurrence probabilities. Discrete Appl. Math. 104 (2000) 259–280, Combinatorial molecular biology. [CrossRef] [MathSciNet] [Google Scholar]
  26. M. Régnier and A. Denise, Rare events and conditional events on random strings. Discrete Math. Theor. Comput. Sci. 6 (2004) 191–213 (electronic). [Google Scholar]
  27. M. Régnier and W. Szpankowski, On pattern frequency occurrences in a Markovian sequence. Algorithmica 22 (1998) 631–649. [CrossRef] [MathSciNet] [Google Scholar]
  28. G. Reinert, S. Schbath and M.S. Waterman, Applied Combinatorics on Words. In Encyclopedia of Mathematics and its Applications, Vol. 105, chap. Statistics on Words with Applications to Biological Sequences. Cambridge University Press (2005). [Google Scholar]
  29. S. Robin and J.-J. Daudin, Exact distribution of word occurrences in a random sequence of letters. J. Appl. Probab. 36 (1999) 179–193. [CrossRef] [MathSciNet] [Google Scholar]
  30. E. Roquain and S. Schbath, Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary Markov chain. Adv. Appl. Probab. 39 (2007) 128–140. [CrossRef] [Google Scholar]
  31. S. Schbath, Compound Poisson approximation of word counts in DNA sequences. ESAIM: PS 1 (1997) 1–16. [CrossRef] [EDP Sciences] [Google Scholar]
  32. D. Serre, Matrices, volume 216 of Graduate Texts Math.. Springer-Verlag, New York (2002). Theory and applications, translated from the 2001 French original. [Google Scholar]
  33. V.T. Stefanov, S. Robin and S. Schbath, Waiting times for clumps of patterns and for structured motifs in random sequences. Discrete Appl. Math. 155 (2007) 868–880. [CrossRef] [MathSciNet] [Google Scholar]

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