Abstract:
Let X1,…,Xm,Y1,…,Yn be independent identically distributed random variables with discrete state space. We estimate the rate of convergence in the limit theorems for the number of long match patterns and for the length of the longest match pattern in random sequences X1,…,Xm,Y1,…,Yn. The results improve the corresponding ones received by Zubkov–Mikhailov, Arratia–Gordon–Waterman, and others.
Citation:
S. Yu. Novak, “Poisson approximation for the number of long match patterns in random sequences”, Teor. Veroyatnost. i Primenen., 39:4 (1994), 731–742; Theory Probab. Appl., 39:4 (1994), 593–603
\Bibitem{Nov94}
\by S.~Yu.~Novak
\paper Poisson approximation for the number of long match patterns in random sequences
\jour Teor. Veroyatnost. i Primenen.
\yr 1994
\vol 39
\issue 4
\pages 731--742
\mathnet{http://mi.mathnet.ru/tvp3850}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1347649}
\zmath{https://zbmath.org/?q=an:0847.60016}
\transl
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 4
\pages 593--603
\crossref{https://doi.org/10.1137/1139045}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TR71500005}
Linking options:
https://www.mathnet.ru/eng/tvp3850
https://www.mathnet.ru/eng/tvp/v39/i4/p731
This publication is cited in the following 5 articles:
C&H/CRC Monographs on Statistics & Applied Probability, 20114852, Extreme Value Methods with Applications to Finance, 2011, 351
V. G. Mikhailov, “A Poisson-Type Limit Theorem for the Number of Pairs of Matching Sequences”, Theory Probab. Appl., 53:1 (2009), 106–116
A. M. Shoitov, “The Poisson approximation for the number of matches of values of a discrete function from chains”, Discrete Math. Appl., 15:3 (2005), 241–254
V. G. Mikhailov, “Poisson-type Limit Theorems for the Number of Incomplete Matches of S-patterns”, Theory Probab. Appl., 47:2 (2003), 343
V. G. Mikhailov, “Estimate of the Accuracy of the Compound Poisson Approximation for the Distribution of the Number of Matching Patterns”, Theory Probab. Appl., 46:4 (2002), 667–675
Citation in format AMSBIB
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