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.
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Athreya, K., MacDonald, D., Ney, P.: Limit theorems for semi-Markov processes and renewal theory for Markov chains. Ann. Probab.6, 788–797 (1978)
Brown, S.: Optimal search for a moving target in discrete time and space. Oper. Res.28, 1275–1289 (1980)
Fitzgerald, C.: The princess and monster differential game. SIAM J. Control Optimization17, 700–712 (1979)
Gal, S.: Search games with mobile and immobile hider. SIAM J. Contol Optimization17, 99–122 (1979)
Gal, S.: Search games. New York: Academic Press 1980
Guillemin, V., Pollack, A.: Differential Tonology. Englewood Cliffs, NJ: Prentice-Hall 1974
Isaacs, R.: Differential games. New York: Wiley 1967
Kesten, H.: Renewal theory for functionals of a Markov chain with general state space. Ann. Probab.2, 355–386 (1974)
Lalley, S., Robbins, H.: Asymptotically minimax stochastic search strategies in the plane. Proc. Natl. Acad. Sci. USA (1987)
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
Orey, S.: Change of time scale for Markov processes. Trans. Am. Math. Soc.99, 384–390 (1961)
Revuz, D.: Markov Chains. Amsterdam: North-Holland 1975
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Supported by NSF grant DMS 82-01723
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Lalley, S., Robbins, H. Stochastic search in a convex region. Probab. Th. Rel. Fields 77, 99–116 (1988). https://doi.org/10.1007/BF01848133
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DOI: https://doi.org/10.1007/BF01848133