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Mot-clé: Markov chain model

[1] Banjevic, D. On some statistics connected with runs in markov chains. J. Appl. Prob. 25 (1988), 815-821.

[2] Benevento, R. The occurrence of sequence patterns in ergodic markov chains. Stoch. Proc. Appl. 17 (1984), 369-373.

[3] Blaisdell, B. E. Markov chain analysis finds a significant influence of neighboring bases on the occurrence of a base in eucariotic nuclear DNA sequences both protein-coding and noncoding. J. Mol. Evol 21 (1985), 278-288.

[4] Erhardsson, T. Compound Poisson approximation for Markov chains. PhD thesis, Royal Institute of Technology, Stockholm, 1997.

[5] Fu, J. C., and Koutras, V. Distribution theory of runs: A Markov chain approach. J. Amer. Statist. Soc. 89 (1994), 1050-1058.

[6] Gerber, H. U., and Li, S.-Y. The occurrence of sequence patterns in repeated experiments and hitting times in a markov chain. Stoch. Proc. Appl. 11 (1981), 101-108.

[7] Geske, M. X., Godbole, A. P., Schaffner, A. A., Skolnick, A. M., and Wallstrom, G. L. Compound Poisson approximations for word patterns under Markovian hypotheses. J. Appl. Prob. 32 (1995), 877-892.

[8] Hirano, K., and Aki, S. On number of occurrences of sucess runs of specified length in a two-state Markov chain. Statistica Sinica 3 (1993), 313-320.

[9] Kleffe, J., and Borodovsky, M. First and second moment of counts of words in random texts generated by Markov chains. Comp. Applic. Biosci. 8 (1992), 433-441.

[10] Kleffe, J., and Langbecker, U. Exact computation of pattern probabilities in random sequences generated by Markov chains. Comp. Applic. Biosci. 6 (1990), 347-353.

[11] Leung, M. Y. Marsh, G. M., and Speed, T. P. Over and underrepresentation of short DNA words in herpesvirus genomes. J. Comp. Biol. 3 (1996), 345-360.

[12] Lundstrom, R. Stochastic models and statistical methods for DNA sequence data. PhD thesis, University of Utah, 1990.

[13] Meyn, S. P., and Tweedie, R. L. Markov chains and stochastic stability. Springer-Verlag, 1993.

[14] Pevzner, P. A. Nucleotide sequences versus Markov models. Computers Chem. 16 (1992), 103-106.

[15] Phillips, G. J., Arnold, J., and Ivarie, R. The effect of codon usage on the oligonucleotide composition of the e. coli genome and identification of over- and underrepresented sequences by Markov chain analysis. Nucl. Acids Res. 15 (1987), 2627-2638.

[16] Phillips, G. J., Arnold, J., and Ivarie, R. Mono- through hexanucleotide composition of the escherichia coli genome : a Markov chain analysis. Nucl. Acids Res. 15 (1987), 2611-2626.

[17] Raftery, A., and Tavaré, S. Estimation and modelling repeated patterns in high order Markov chains with the Mixture Transition Distribution Model. Appl. Statist. 43 (1994), 179-199.

[18] Raftery, A. E. A model for high-order Markov chains. J. R. Statist. Soc. B 47 (1985), 528-539.

[19] Rajarshi, M. B. Success runs in a two-state Markov chain. J. Appl. Prob. 11 (1974), 190-192.

[20] Reinert, G., and Schbath, S. Compound Poisson and Poisson process approximations for occurrences of multiple words in markov chains. J. Comp. Biol. 5 (1998), 223-254.

[21] Rudander, J. On the first occurrence of a given pattern in a semi-Markov process. PhD thesis, University of Uppsala, 1996.

[22] Samarova, S. On the length of the longest head run for a markov chain with two states. Theory Prob. Appl. 26 (1981), 498-509.

[23] Schbath, S. Étude asymptotique du nombre d'occurrences d'un mot dans une chaîne de Markov et application à la recherche de mots de fréquence exceptionnelle dans les séquences d'ADN. PhD thesis, Université René Descartes, Paris V, 1995.

[24] Schbath, S., Prum, B., and Turckheim, E. d. Exceptional motifs in different Markov chain models for a statistical analysis of DNA sequences. J. Comp. Biol. 2 (1995), 417-437.

[25] Schwager. Run probabilities in sequences of markov-dependent trials. J. Amer. Statist. Soc. 78 (1983), 168-175.

[26] Tanushev, M. S. Central limit theorem for several patterns in a markov chain sequence of letters. Preprint, 1996.

[27] Whittle, P. Some distribution and moment formulae for the Markov chain. J. R. Statist. Soc. B 17 (1955), 235-242.

Fri Feb 11 09:39:23 MET 2000

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