RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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., 1964, Volume 9, Issue 4, Pages 746–753 (Mi tvp429)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

Uniformly-Optimal Strategies in Search Problems

V. I. Arkin

Moscow

Abstract: Let $f(x)$ be the density function of the a priori distribution of a particle in $R^n$. The strategy of search is defined by a function $\alpha=\alpha(x,t)\geqq 0$, $\int_{R^n}\alpha(x,t) dx=1$. The probability of finding the particle at a point $x$ during time $t$, under the condition that it is there, using the strategy $\alpha$, is given by the functional II $(\int_0^t\alpha(x,t) dt,x)$. Let $P_\alpha(T)$ be the probability of finding the particle using the strategy $\alpha$ during the time $T$. A strategy $\alpha^*$ is uniformly optimal if $P_{\alpha^*}(T)=\sup\limits_\alpha P_\alpha (T)$ for any $T>0$. In a very general case we prove the existence of the strategy $\alpha^*$ and find its explicit form.

Full text: PDF file (442 kB)

English version:
Theory of Probability and its Applications, 1964, 9:4, 674–680

Bibliographic databases:

Received: 01.07.1964

Citation: V. I. Arkin, “Uniformly-Optimal Strategies in Search Problems”, Teor. Veroyatnost. i Primenen., 9:4 (1964), 746–753; Theory Probab. Appl., 9:4 (1964), 674–680

Citation in format AMSBIB
\Bibitem{Ark64}
\by V.~I.~Arkin
\paper Uniformly-Optimal Strategies in Search Problems
\jour Teor. Veroyatnost. i Primenen.
\yr 1964
\vol 9
\issue 4
\pages 746--753
\mathnet{http://mi.mathnet.ru/tvp429}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=170756}
\zmath{https://zbmath.org/?q=an:0136.14602}
\transl
\jour Theory Probab. Appl.
\yr 1964
\vol 9
\issue 4
\pages 674--680
\crossref{https://doi.org/10.1137/1109095}


Linking options:
  • http://mi.mathnet.ru/eng/tvp429
  • http://mi.mathnet.ru/eng/tvp/v9/i4/p746

    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

    This publication is cited in the following articles:
    1. Strotsev A.A., Yunusmetov R.A., Shvalov D.V., “Matematicheskaya model poiskovykh usilii gruppovoi poiskovoi sistemy so sfericheskimi sredstvami nablyudeniya”, Vestn. Rostovskogo gos. un-ta putei soobscheniya, 2009, no. 3, 62–70
    2. Ruslekov A.A., “Metodologiya otsenki effektivnosti strelby na osnove teorii optimalnogo upravleniya”, Izvestiya rossiiskoi akademii raketnykh i artilleriiskikh nauk, 2011, no. 67, 62–66  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:179
    Full text:96

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020