On the length of the longest run in a multi-state Markov chain

Statistics and Probability Letters

Volumn 62, Issue 3, 2003, Pages 211-221

  Vaggelatou, Eutichia ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Erd s Renyi type law; Extreme value distribution; Longest run; Multi state trials

Indexed keywords

EID: 0037445844     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(02)00432-7     Document Type: Article

References (23)

1. Arratia, R., Goldstein, L., Gordon, L., 1989. Two moments suffice for Poisson approximation. Ann. Probab. 17, 9-25.
2. Arratia, R., Goldstein, L., Gordon, L., 1990. Poisson approximation and the Chen-Stein method. Statist. Sci. 5, 403-434.
3. Balakrishnan, N., Koutras, M.V., 2001. Runs and Scans with Applications, 1st Edition. Wiley, New York.
4. Barbour, A.D., Holst, L., Janson, S., 1992. Poisson Approximation. Oxford University Press, Oxford.
5. Chryssaphinou, O., Papastavridis, S., Vaggelatou, E., 2001. Poisson approximation for the non-overlapping appearances of several words in Markov chains. Combinatorics Probab. Comput. 10, 293-308.
6. Darling, R.W.R., Waterman, M.S., 1986. Extreme value distribution for the largest cube in a random lattice. SIAM J. Appl. Math. 46, 118-132.
7. Erdös, P., Renyi, A., 1970. On a new law of large numbers. J. Anal. Math. 23, 103-111.
8. Erdös, P., Révész, P., 1975. On the length of the longest head-run. In: Csiszár, I. (Ed.), Topics in Information Theory. Colloq. Math. Soc. János Bolyai, Budapest, pp. 219-228.
9. Földes, A., 1979. The limit distribution of the length of the longest head run. Period. Math. Hungarica 10, 301-310.
10. Fu, J.C., 1996. Distribution theory of runs and patterns associated with a sequence of multi-state trials. Statist. Sinica 6, 957-974.
11. Goncharov, V.L., 1943. On the field of combinatory analysis. Amer. Math. Soc. Transl. 19, 1-46.
12. Gordon, L., Schilling, M.F., Waterman, M.S., 1986. An extreme value theory for long head runs. Probab. Theory Relat. Fields 72, 279-287.
13. Grill, K., 1987. Erdös-Révész type bounds for the length of the longest run from a stationary mixing sequence. Probab. Theory Relat. Fields 75, 77-85.
14. Guibas, L.J., Odlyzko, A.M., 1980. Long repetitive patterns in random sequence. Z. Wahrsch. Verw. Geb. 53, 241-262.
15. Kusolitsch, N., 1982. Longest runs in Markov chains. In: Grossman, W., et al. (Ed.), Probability and Statistical Inference. Reidel, Dordrecht, pp. 223-230.
16. Kusolitsch, N., Nemetz, T., 1982. Erdös-Révész type asymptotic bounds and the length of longest paths in certain random graphs. Colloq. Math. Soc. János Bolyai 36. Limit theorems in Probability and Statistics, Veszprém, Hungary, pp. 649-665.
17. Lou, W.Y.W., 1996. On runs and longest run tests: a method of finite Markov chain imbedding. J. Amer. Statist. Assoc. 91, 1595-1601.
18. Nemetz, T., Kusolitsch, N., 1982. On the longest run of coincidences. Z. Wahrsch. Verw. Geb. 61, 59-73.
19. Novak, S.Yu., 1988. Time intervals of constant sojourne of an homogeneous Markov chain in a fixed subset of states. Sib. Math. J. 29, 100-109.
20. Novak, S.Yu., 1989. Asymptotic expansions in the problem of the longest head-run for Markov chain with two states. Tr. Inst. Mat. 13, 136-147.
21. Novak, S.Yu., 1992. Longest runs in a sequence of m-dependent random variables. Probab. Theory Relat. Fields 91, 269-281.
22. Samarova, S.S., 1981. On the length of the longest head-run for a Markov chain with two states. Theory Probab. Appl. 26, 498-512.
23. Variakoyis, L., 1986. On the maximal length of "success" run in a countable Markov chain. Lit. Math. J. 26, 605-615.