Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Stochastic search in a convex region
Download PDF
Download PDF
  • Published: March 1988

Stochastic search in a convex region

  • Steven Lalley1 &
  • Herbert Robbins2 

Probability Theory and Related Fields volume 77, pages 99–116 (1988)Cite this article

  • 89 Accesses

  • 21 Citations

  • Metrics details

Summary

A stochastic search strategy is proposed for locating a possibility mobile target in a bounded, convex region of the plane. The strategy is asymptotically minimax as ε→0 with respect to the time required to get within ε of the target. The proof involves the study of first passages to time-dependent boundaries by a certain semi-Markov process.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Athreya, K., MacDonald, D., Ney, P.: Limit theorems for semi-Markov processes and renewal theory for Markov chains. Ann. Probab.6, 788–797 (1978)

    Google Scholar 

  2. Brown, S.: Optimal search for a moving target in discrete time and space. Oper. Res.28, 1275–1289 (1980)

    Google Scholar 

  3. Fitzgerald, C.: The princess and monster differential game. SIAM J. Control Optimization17, 700–712 (1979)

    Google Scholar 

  4. Gal, S.: Search games with mobile and immobile hider. SIAM J. Contol Optimization17, 99–122 (1979)

    Google Scholar 

  5. Gal, S.: Search games. New York: Academic Press 1980

    Google Scholar 

  6. Guillemin, V., Pollack, A.: Differential Tonology. Englewood Cliffs, NJ: Prentice-Hall 1974

    Google Scholar 

  7. Isaacs, R.: Differential games. New York: Wiley 1967

    Google Scholar 

  8. Kesten, H.: Renewal theory for functionals of a Markov chain with general state space. Ann. Probab.2, 355–386 (1974)

    Google Scholar 

  9. Lalley, S., Robbins, H.: Asymptotically minimax stochastic search strategies in the plane. Proc. Natl. Acad. Sci. USA (1987)

  10. Lalley, S., Robbins, H.: Stochastic search in a square and on a torus. In: Berger, J., Gupta, S. (eds.) Proc. 4th Purdue Symp. Statist. Dec. Th. 1986

  11. Orey, S.: Change of time scale for Markov processes. Trans. Am. Math. Soc.99, 384–390 (1961)

    Google Scholar 

  12. Revuz, D.: Markov Chains. Amsterdam: North-Holland 1975

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Statistics Department, Math Sciences Building, Purdue University, 47907, West Lafayette, IN, USA

    Steven Lalley

  2. Department of Statistics, Rutgers University, 08903, New Brunswick, NJ, USA

    Herbert Robbins

Authors
  1. Steven Lalley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Herbert Robbins
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by NSF grant DMS 82-01723

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lalley, S., Robbins, H. Stochastic search in a convex region. Probab. Th. Rel. Fields 77, 99–116 (1988). https://doi.org/10.1007/BF01848133

Download citation

  • Received: 10 April 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF01848133

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Probability Theory
  • Search Strategy
  • Mathematical Biology
  • Stochastic Search
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature