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More on the Waiting Time Till Each of Some Given Patterns Occurs as a Run

Published online by Cambridge University Press:  20 November 2018

Tamás F. Móri
Tamás F. Móri*
Affiliation:
Eötvös University, Budapest, Múzeum krt. 6-8, H-1088 Hungary
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Let H be a finite set; we can suppose H = { 1, 2, …,d } . Consider Hn, the set of length n words over the alphabet H. For every A ∈ Hn define the waiting time for A as the number of experiments needed till A appears as a connected sub-sequence of random elements of H. Formally, let X1, X2,... be i. i. d. random variables, P(X1 = i) = d−1, 1 ≤ i ≤ d then

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 5 , 01 October 1990 , pp. 915 - 932
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Benczúr, A., On the expected time to the first occurence of every k bit long pattern in the symmetricBernoulli process, Acta Math., Hungar. 47 (1986) 233–238.Google Scholar
2. Erdõs, P., and Révész, P., On the length of the longest head run. In: Topics in Information Theory, (Keszthely, Hungary, 1975), Colloq. Math. Soc. J. Bolyai, 16 (1977) 219–228.Google Scholar
3. Galambos, J., The Asymptotic Theory of Extreme Order Statistics, (1978) Wiley, New York.Google Scholar
4. Guibas, L.J., and Odlyzko, A.M., Long repetitive patterns in random sequences, Z. Wahrsch. verw. Geb., 53 (1980) 241–262.Google Scholar
5. Li, S.R., A martingale approach to the study of occurence of sequence patterns in repeated experiments,, Ann. Prob. 8 (1980) 1171–1176.Google Scholar
6. Mori, T.F., Large deviation results for waiting times in repeated experiments, Acta Math. Hungar., 45 (1985)213–221.Google Scholar
7. Móri, T.F., On the expectation of the maximum waiting time, Ann. Univ. Sci. Bud. R. Eötvös Nom., Sect.Comput.,7 (1987) 111–115.Google Scholar
8. Móri, T.F., Asymptotic joint distribution of waiting times in repeated experiments , Lecture read at the 4th EYSM, Varna, Bulgaria, (1985).Google Scholar
9. Móri, T.F., On the waiting time till each of some given patterns occurs as a run , Prob. Th. Rel. Fields, to appear.Google Scholar
10. Móri, T.F., and Székely, G.J., Asymptotic independence of ‘pure head’ stopping times, Statist. Prob. Letters, 2 (1984) 5–8.Google Scholar
11. Neveu, J., Discrete Parameter Martingales, North-Holland, Amsterdam, (1975).Google Scholar
12. Révész, P., Strong theorems on coin tossing , In: Proc. 1978 Internat. Congress of Mathematicians, Helsinki, (1980)749–754.Google Scholar