On the Distribution of the Time up to the First Occurrence of a Given Number of Different $\ell $-Tuple Series

Иванов, В. А.; Novikov, Andrei

doi:10.1137/1122063

Cited by 8 publications

(3 citation statements)

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“…Ivanov and Novikov [3]), or by using general theorems on Poisson approximation such as Theorem 1 of Sevast'yanov [7].…”

Section: And N Tend To Infinity Such That N Exp (--N-kn)---)>o Thementioning

confidence: 99%

Large deviation results for waiting times in repeated experiments

Móri

1985

Acta Math Hung

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“…Ivanov and Novikov [3]), or by using general theorems on Poisson approximation such as Theorem 1 of Sevast'yanov [7].…”

Section: And N Tend To Infinity Such That N Exp (--N-kn)---)>o Thementioning

confidence: 99%

Large deviation results for waiting times in repeated experiments

Móri

1985

Acta Math Hung

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“…Alternately, one can appeal to Aldous's (1989) clumping heuristic to get Poisson convergence, but neither method easily gives rates of convergence. Related work (without rates, and primarily dealing with long runs) can be found in Wolfowitz (1944), Olmstead (1958), Burr and Cane (1961), Sevastyanov (1972), Zubkov and Mikhailov (1974), Ivanov and Novikov (1977), Foldes (1979), Papastavridis (1991) and Chryssaphinouand Papastavridis (1988a,b).…”

Section: Introductionmentioning

confidence: 99%

Poisson approximations for runs and patterns of rare events

Godbole¹

1991

Advances in Applied Probability

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Consider a sequence of Bernoulli trials with success probability p, and let Nn,k denote the number of success runs of length among the first n trials. The Stein–Chen method is employed to obtain a total variation upper bound for the rate of convergence of Nn,k to a Poisson random variable under the standard condition npk→λ. This bound is of the same order, O(p), as the best known for the case k = 1, i.e. for the classical binomial-Poisson approximation. Analogous results are obtained for occurrences of word patterns, where, depending on the nature of the word, the corresponding rate is at most O(pk–m) for some m = 0, 2, ···, k – 1. The technique is adapted for use with two-state Markov chains. Applications to reliability systems and tests for randomness are discussed.

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“…In Odlyzko (1980), (1981) a combinatorial approach to these and some other problems is c()n~idered.ln Li (198()) and Gerber and Li (1981) a Markov~e<\\lence of ex.\lerime\\t~ic onsidered, and a martingale approach for investigation of waiting times is used. In Solov'eov (1966), Ivanov and Novikov (1977), Mori and Szekely (1984) (1985), results on limiting distributions of some waiting times for sequence patterns are given. Rade (1976) and Glick (1981) obtained some results about waiting times for some simple sequence patterns.…”

Section: Introduction and Review Of The Literaturementioning

confidence: 99%