Application of a Functional Equation to a Class of Stochastic Detection Models

Barry Belkin
Additional contact information
Barry Belkin: Daniel H. Wagner, Associates, Paoli, Pennsylvania

Operations Research, 1975, vol. 23, issue 6, 1143-1154

Abstract: In a proposed class of abstract stochastic detection models, the occurrence of detection is related to the time-dependent behavior of a detection functional defined on the signal-to-noise process sample paths. We describe a potential operations-analysis application in certain sonar detection problems. The method developed for computing detection probabilities for these models requires the solution of a functional equation involving the detection functional and the weak infinitesimal operator of the signal-to-noise process, assumed Markovian with stationary transition probabilities. Two hypothetical signal-to-noise processes considered in detail are the random sampling process and the stationary Gauss-Markov (Ornstein-Uhlenbeck) process in the special case when the detection functional measures time above a constant threshold level. We compare expressions for the mean time to detect, obtained for these processes, numerically.

Date: 1975
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/opre.23.6.1143 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:23:y:1975:i:6:p:1143-1154

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().