Geodesic
Asymptotic normality of the number of absent noncontinuous chains of outcomes of independent trials
Diskretnaya Matematika, Tome 21 (2009) no. 2, pp. 112-125.

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We prove the asymptotic normality of the number of absent noncontinuous chains (chains with gaps) of outcomes of independent trials. The asymptotic normality of the number of absent chains of identical outcomes, which has been proved for equiprobable outcomes, is proved in the nonequiprobable case. 
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M. I. Tikhomirova. Asymptotic normality of the number of absent noncontinuous chains of outcomes of independent trials. Diskretnaya Matematika, Tome 21 (2009) no. 2, pp. 112-125. http://geodesic.mathdoc.fr/item/DM_2009_21_2_a7/

[1] Tikhomirova M. I., “Ob asimptoticheskoi normalnosti chisla nepoyavivshikhsya $s$-tsepochek”, Diskretnaya matematika, 4:2 (1992), 122–129 | MR | Zbl

[2] Tikhomirova M. I., Chistyakov V. P., “Ob asimptotike momentov chisla nepoyavivshikhsya $s$-tsepochek”, Diskretnaya matematika, 9:1 (1997), 12–29 | MR | Zbl

[3] Tikhomirova M. I., Predelnye teoremy dlya chisla nepoyavivshikhsya $s$-tsepochek, Dissertatsiya na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk, MIEM, Moskva, 1998

[4] Mikhailov V. G., “Asimptoticheskaya normalnost razdelimykh statistik ot chastot $m$-tsepochek”, Diskretnaya matematika, 1:4 (1989), 92–103 | MR | Zbl

[5] Tikhomirova M. I., “Predelnye raspredeleniya chisla nepoyavivshikhsya tsepochek odinakovykh iskhodov”, Diskretnaya matematika, 20:3 (2008), 40–46 | MR | Zbl

[6] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, T. 1, Mir, Moskva, 1984 | Zbl

[7] Bernshtein C. N., Sobranie sochinenii, T. 4, Nauka, Moskva, 1964

[8] Janson S., “Normal convergence by higher semiinvariants with application to sums of dependent random variables and random graphs”, Ann. Probab., 16:1 (1988), 305–312 | DOI | MR | Zbl

[9] Mikhailov V. G., “Ob odnoi teoreme Yansona”, Teoriya veroyatnostei i ee primeneniya, 36:1 (1991), 168–170 | MR | Zbl