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On the optimal search for a target whose motion is a Markov process

Published online by Cambridge University Press:  14 July 2016

Lauri Saretsalo
Lauri Saretsalo*
Affiliation:
University of Jyväskylä, Finland
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Abstract

We will consider the optimal search for a target whose motion is a Markov process. The classical detection law leads to the use of multiplicative functionals and the search is equivalent to the termination of the Markov process with a termination density. A general condition for the optimality is derived and for Markov processes in n-dimensional Euclidean space with continuous transition functions we derive a simple necessary condition which generalizes the result of Hellman (1972).

Keywords

OPTIMAL SEARCHMARKOV PROCESS MODEL FOR MOVING TARGETSCLASSICAL DETECTION LAWTERMINATION OF MARKOV PROCESSESNECESSARY CONDITION FOR OPTIMAL SEARCH DENSITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 847 - 856
Copyright
Copyright © Applied Probability Trust 1973 

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References

Arkin, V. I. (1964) Uniformly optimal strategies in search problems. Theor. Probability Appl. 9, 674–680.Google Scholar
De Guenin, J. (1961) Optimum distribution of effort: An extension of the Koopman basic theory. Operations Res. 9, 1–7.Google Scholar
Dynkin, E. B. (1960) Theory of Markov Processes. Pergamon Press, London.Google Scholar
Dubovitskii, A. and Milyutin, A. (1965) Extremum problems in the presence of constraints. Zh. Vychisl. Mat. i. Mat. Fiz. 5, 395–453 (in Russian).Google Scholar
Hellman, O. B. (1970) On the effect of search upon the probability distribution of a target whose motion is a diffusion process. Ann. Math. Statist. 41, 1717–1724.Google Scholar
Hellman, O. B. (1972) On the optimal search for a randomly moving target. SIAM J. Appl. Math. 22, 545–552.Google Scholar
Kac, M. (1959) Probability and Related Topics in Physical Sciences. Interscience, London.Google Scholar
Koopman, B. O. (1957) The theory of search III. The optimum distribution of searching effort. Operations Res. 5, 613–626.Google Scholar
Perko, A. (1971) Some problems of search and detection. Report 21, Institute for Applied Mathematics, University of Turku, Finland (Dissertation).Google Scholar
Pursiheimo, U. (1972) On the optimal search for a moving target. Report 35, Institute for Applied Mathematics, University of Turku, Finland.Google Scholar
Saretsalo, L. O. (1971) On stochastic models of search for stationary and moving objects. Publications of the Institute for Applied Mathematics 2, University of Turku, Finland (Dissertation).Google Scholar
Saretsalo, L. O. (1972) On the search for a target whose motion is a Markov process. Report 30, Institute for Applied Mathematics, University of Turku, Finland. (Submitted for publication.) Google Scholar