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A stochastic ordering and related sequential decision problems. (English) Zbl 0707.90096

A partial order (\(\geq)\) is defined for probability measures on the state space of a discrete time Markov process. It is supposed that the current state s of the process is indicated only by a realisation x of a random variable with distribution \(P_ s\). Under various monotonicity conditions on the transition function and \(P_ s\), it is shown that the Bayesian posterior distribution of the state is increasing (in the sense of \(\geq)\) in both x and the prior. These notions are then applied to obtain structural properties of some partially observed Markov decision processes: job search, sequential stochastic assignment and replacement.
Reviewer: J.Preater

MSC:

90C40 Markov and semi-Markov decision processes
62L15 Optimal stopping in statistics
90B25 Reliability, availability, maintenance, inspection in operations research
90C90 Applications of mathematical programming
91B40 Labor market, contracts (MSC2010)
60G40 Stopping times; optimal stopping problems; gambling theory
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References:

[1] Aström K.J., Journal of Mathematical Analysis and Applications 26 pp 35– (1966)
[2] De Vylder F., Scandinavian Actuarial Journal pp 129– (1983) · Zbl 0522.62087
[3] Doob J.L., Stochastic Process (1953)
[4] Feller W., An Introduction to Probability Theory and Applications 1 (1950) · Zbl 0039.13201
[5] Lippman S.A., Economic Inquiry 14 pp 155– (1976)
[6] Nakai T., Journal of Optimization Theory and Applications 45 pp 425– (1985) · Zbl 0543.60054
[7] Nakai T., Mathematics of Operations Research 11 pp 230– (1986) · Zbl 0601.90137
[8] Ohnishi M., Europian Journal of Operations Research 27 pp 117– (1986) · Zbl 0623.90025
[9] Ross S.M., Applied Probability with Optimization Applications (1970) · Zbl 0213.19101
[10] Ross S.M., Stochastic Processes (1983)
[11] Whitt W., Journal of Applied Probability 17 pp 112– (1980)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.