Probability Theory and Related Fields

, Volume 77, Issue 1, pp 99–116

Stochastic search in a convex region

  • Steven Lalley
  • Herbert Robbins

DOI: 10.1007/BF01848133

Cite this article as:
Lalley, S. & Robbins, H. Probab. Th. Rel. Fields (1988) 77: 99. doi:10.1007/BF01848133


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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Steven Lalley
    • 1
  • Herbert Robbins
    • 2
  1. 1.Statistics Department, Math Sciences BuildingPurdue UniversityWest LafayetteUSA
  2. 2.Department of StatisticsRutgers UniversityNew BrunswickUSA