RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 1, Pages 59–71 (Mi tvp319)  

A Poisson-Type Limit Theorem for the Number of Pairs of Matching Sequences

V. G. Mikhailov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Two sequences $X_1,…,X_m$ and $Y_1,…,Y_n$ are considered constituted by independent identically distributed random variables within each of the sequences taking on values in the set $\{1,2,…\}$. We study the distribution of the number $N_d$ of such pairs of $s$-patterns $(\overline X_i,\overline Y_j)$, where $\overline X_i=(X_i,…,X_{i+s-1})$, $\overline Y_j=(Y_j,…,Y_{j+s-1})$, in which the $s$-patterns $\overline X_i$ and $\overline Y_j$ differ by a relatively small number of elements $d$. It is shown that if ${m,n,s\to\infty}$, $d=o(s/\log s),$ and the distributions of the elements of the sequences vary in such a way that the probability $P\{X_i=Y_j\}$ and $EN_d$ converge to some limiting values, then the distribution of $N_d$ converges to a compound Poisson distribution. The value of the parameter $d$ plays a role only to provide, passing to the limit, the needed rate of the parameters involved and has no influence on the form of the limit distribution. This limit distribution has the same form as that for the number of pairs $(\overline X_i,\overline Y_j)$, in which $\overline X_i=\overline Y_j$.

Keywords: $s$-patterns, pattern matching, mismatches of patterns, Poisson limit theorem, compound Poisson distribution, Chen-Stein method.

DOI: https://doi.org/10.4213/tvp319

Full text: PDF file (1021 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2009, 53:1, 106–116

Bibliographic databases:

Document Type: Article
Received: 12.12.2005
Revised: 15.05.2007

Citation: V. G. Mikhailov, “A Poisson-Type Limit Theorem for the Number of Pairs of Matching Sequences”, Teor. Veroyatnost. i Primenen., 53:1 (2008), 59–71; Theory Probab. Appl., 53:1 (2009), 106–116

Citation in format AMSBIB
\Bibitem{Mik08}
\by V.~G.~Mikhailov
\paper A Poisson-Type Limit Theorem for the Number of Pairs of Matching Sequences
\jour Teor. Veroyatnost. i Primenen.
\yr 2008
\vol 53
\issue 1
\pages 59--71
\mathnet{http://mi.mathnet.ru/tvp319}
\crossref{https://doi.org/10.4213/tvp319}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2760565}
\zmath{https://zbmath.org/?q=an:05701593}
\transl
\jour Theory Probab. Appl.
\yr 2009
\vol 53
\issue 1
\pages 106--116
\crossref{https://doi.org/10.1137/S0040585X97983390}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000264940300006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-62249188893}


Linking options:
  • http://mi.mathnet.ru/eng/tvp319
  • https://doi.org/10.4213/tvp319
  • http://mi.mathnet.ru/eng/tvp/v53/i1/p59

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:161
    Full text:14
    References:43

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019